chuyen de khao sat ham so 12 day hoc 2015 khao sat ham so chuong 1

Gia s Thnh c www.daythem.edu.vn ễN TP NHNG KIN THC CN NH VN DNG GII TON Vn CễNG THC TNH O HM (x a )' = a x a- 1 ( x )' = x ' ổ1 = - ỗỗ ữ ữ ốx ứ x a a (e )' = u '.e ( ) (a )' = a ln a a (a )' = u '.a ex ' = ex a- a (u )' = a u u ' u' a ( u )' = u ' ổ1 u' a ỗỗ ữ = - ữ ốu ứ u x x u u u u ln a ( ) u v ' = u '.v + v '.u ' ổu u '.v - v ' u ữ ỗỗ ữ = ữ ỗốv ứ ữ v2 (sin x )' = cos x (cos x ) ' = - sin x x (ln x )' = x a (sin u )' = u ' cos u a (cos x ) ' = - u ' sin u u' (t an x )' = a (t an u )' = cos x cos2 u u' (cot x )' = a (cot u )' = sin x sin u u' u u' a (ln u )' = u (ln x )' = (loga x )' = a (ln u )' = u' a (loga u )' = x ln a u ln a Vn CễNG THC LNG GIC H t n sin x + cos2 x = sin x t an x = cos x + t an x = c os2x n C n t n n un C n t cos (a b) = cos a cos b m sin a sin b t an a + t an b t an (a + b) = - t an a t an b t an a - t an b t an (a - b) = + t an a t an b n tn t n cos a sin a + sin a - n t C n t n tn t n t a+b a- b cos 2 a+b a- b cos b = - sin sin 2 a+b a- b sin b = sin cos 2 a+b a- b sin b = cos sin 2 a t n sin a , cos a theo t = t an cos a + cos b = cos sin (a b) = sin a cos b cos a sin b C n t n sin 2x = sin x cos x cos 2x = cos2 x - sin x = cos2 x - = - sin x - cos 2x + cos 2x ; cos2 x = ị sin x = 2 sin s n sin 3x = sin x - sin x c cụ) cos 3x = cos3 x - cos x tan x cot x = cos x cot x = sin x + cot x = sin x C n t n Gia s Thnh c www.daythem.edu.vn ớù 2t ùù sin a = 1+ t2 ùù ùù 1- t2 a t t = t an ị ùỡ cos a = ùù 1+ t2 ùù ùù t an a = 2t ùù 1- t2 ợ M t s n t 1ộ cos (a - b) + cos (a + b)ự ỳ ỷ ờở sin a cos b = ộờsin (a - b) + sin (a + b)ự ỳ ỷ 2ở cos a cos b = sin a sin b = 1ộ cos (a - b)- cos (a + b)ự ỳ ỷ ờở M t s n t + cos 4x sin 2x = + cos 4x 6 cos x + sin x = - sin 2x = tan x + cot x = sin 2x cot x - tan x = cot 2x cos4 x + sin x = - sin x + cos x = sin x - cos x = ổ sin ỗỗx + ỗố ổ sin ỗỗỗx ố Vn PH NG TR NH LNG GIC C P ổ cos ỗỗx ốỗ ổ cos ỗỗỗx + ố a ộu = v + k 2p : sin u = sin v ờờ ờởu = p - v + k 2p b ộu = v + k 2p : cos u = cos v ờờ ờởu = - v + l 2p c i c t an u = t an v u = v + k p : p ék : u, v + kp c i d : h n tr nh ln N c i ék : u , v k p i cc i n c ớù ùù sin x = ị x = k p ùù ù p + k 2p i t: ùỡ sin x = ị x = ùù ùù p ùù sin x = - ị x = + k 2p ùợ ớù ùù cos x = ị x = p + k p ùù t: ùỡ cos x = ị x = k 2p ùù ùù cos x = - ị x = p + k 2p ùù ợ ớù t an x = x = k p ùù t: ỡ ùù t an x = x = p + k p ùùợ ớù ùù cot x = x = p + k p ù t: ỡ ùù p ùù cot x = x = + k p ùợ n : a sin x + b cos x = c (1) i u ki n c n hi m a + b2 c pử ữ ữ ữ ữ 4ứ pử ữ ữ ữ ữ 4ứ n tr nh l ng giỏc c b n: cot u = cot v u = v + k p pử ữ ữ = ữ ữ 4ứ pử ữ ữ = ữ ữ 4ứ a a + b2 ta c (1) hia hai v cho a +b t sin a = a a +b 2 a +b sin a sin x + cos a cos x = x = a b + k 2p b , cos a = c 2 (a ẻ 2 a +b ộ0, 2p ự ờở ỳ ỷ cos(x - a ) = a +b (k ẻ Â ) b sin x + ) cos x = c a + b2 h n tr nh tr thnh c a + b2 = cos b Gia s Thnh c h n tr nh ln www.daythem.edu.vn i c n c p 2 ng ng: a sin x + b sin x cos x + c cos x = d (2) c hai i m tra m cos x = c ph i l n hi m kh n u c th nh n n hi m n Khi cos x chia hai v ph n tr nh (2) cho cos x ta c a t an x + b t an x + c = d (1 + t an x ) t t = tan x h n tr nh i c hai th o t : (a - d )t + b.t + c - d = đ t đ x a v ph n tr nh n : a (sin x cos x ) + b sin x cos x + c = (3) n ( t t = cos x sin x = cos x m p ; t Ê ) ị t = sin x cos x ị sin x cos x = Tha vo ph n tr nh (3) ta c ph n tr nh h n tr nh i 2 (t - 1) c hai th o t đ t đ x n : a sin x cos x + b sin x cos x + c = (4) n ( p ; éK : Ê t Ê ) t t = cos x sin x = cos x m Gi i t n t nh hi t m x c n lu ph n tr nh ch a n tr n ị sin x cos x = u tr tu t (t - 1) i Vn PH NG TR NH I S P a/ n tr n : ax + bx + c = (1) hai N ub s N ub T nh D = b2 - 4ac u D < 0ị u D = 0ị s T nh D ' = b '2 - ac v i b ' = b u D ' < ị h n tr nh v n hi m u D ' = ị h n tr nh c n hi m h n tr nh v n hi m h n tr nh c n hi m b' a u D ' > ị h n tr nh c hai n hi m ộ ờx = - b '- D ' a ph n i t ờ ờx = - b '+ D ' ờở a k p x = - b 2a u D > ị h n tr nh c hai ộ ờx = - b - D 2a n hi m ph n i t ờ ờx = - b + D ờở 2a k p x = - b/ u ph n tr nh (1) c hai n hi m ph n i t x 1, x th T n hai n hi m S = x + x = - n b a ị x1 - x = c T ch hai n hi m P = x 1.x = a c/ D D' = a a Gia s Thnh c www.daythem.edu.vn ớa ù h n tr nh c hai n hi m ph n i t ùỡ h n tr nh c hai n hi m tr i h n tr nh c hai n hi m ph n i t c n ùù D > ợ u a.c < ớD > ù u ùỡ ùù P > ợ ớù D > ùù ù h n tr nh c hai n hi m m ph n i t ùỡ P > ùù ùù S < ùợ ớù D > ùù ù h n tr nh c hai n hi m n ph n i t ùỡ P > ùù ùù S > ùợ g(x ) = ax + bx + c = v i s t k ớù ớù ùù ùù ùù D > ùù D > ù x > x > b ỡ a g (b ) > x < x < b ùỡ a g (b ) > x < b < x a.g (b ) < ùù ùù ùù S ùù S < b ùù > b ùù ợ ợ2 2 P n tr n ax + b ' x + c ' x + d ' = (2) ộx = a (x - a ) (ax + bx + c ) = ờờ ờởax + bx + c = (3) 2 t g(x ) = ax + bx + c , D = b - 4ac d/ h n tr nh (2) c n hi m ph n i t (3) c h n tr nh (2) c n hi m ph n i t (3) c n hi m k p x a ho c (3) c hai n hi m ph n i t tron P ùớ D > n hi m ph n i t x a ùỡ c h n tr nh (2) c n tr n ùù g(a ) ùợ ộùớ D = ờù ờỡù g(a ) ờùùợ n hi m x = a ờùớ D > ờù ờỡ ờùùùợ g(a ) = ộùớ D = ờù ờỡ n hi m (3) v n hi m ho c (3) c n hi m k p x = a ờùùù g( a ) = ờợ ờD < ờở n tr n p n : ax + bx + c = (4) t t = x éK : t h n tr nh (4) at + bt + c = (5) Gia s Thnh c www.daythem.edu.vn n hi m ph n i t (5) c h n tr nh (4) c h n tr nh (4) c n hi m ph n i t (5) c h n tr nh (4) c n hi m ph n i t (5) c ớù D > ùù ù n hi m n ph n i t ùỡ P > ùù ùù S > ùợ ớù c = ù n hi m t = v n hi m t > ùỡ b ùù - > ùùợ a n hi m tr i u ho c (5) c n hi m k p ộac < ờ n ờùớù D = ờỡ ờùù S > ởợ P n tr n Ph n tr n nt :+ ùớù B A = B ỡ ùù A = B ùợ + ùớ A (hay B 0) B ùỡ ùù A = B ùợ A = ớB u t p n tr n t p n tr n tr tu t : nt : u ù + A = B ùỡ + A = B A = B ùù A = B ợ ộớù B < ờù ờỡù A ờùợ + A B ờớù B ờù ờỡù ờùùợ A B ớù B ùù ù + A Ê B ùỡ A ùù ùù A Ê B ùợ ộA B + A B ờờ ờA Ê - B tr tu t : + A Ê B - B Ê A Ê B Vn H NH H C PH NG Tron m t ph n o cac Oxy cho: n i m A (x A , y A ), B (x B , y B ) , C (xC , yC ) v M (x o , yo ) o n th n D : ax + by + c = o n tr n (C m ) : (x - a ) + (y - b) = R hay (C m ) : x + y - 2ax - 2by + c = c t m l 2 I (a, b) v n k nh l R = a + b2 - c uuur ct A B = (x B - x A ; y B - y A ) ị i o n th n A B = 2 (x B - x A ) + (y B - y A ) A, B) ho n c ch t a i m A (x A , y A ); B (x B , y B ) v C (xC , yC ) th ng hng v i n t ch i ( i m M x o , yo ) xB - xA x - xA = C yB - yA yC - y A n n th n D : ax + by + c = l d (M , D ) = ax o + bx o + c n qua n th n D D l n th n trun tr c c a o n th n S D A BC = uuur uuur 1 A B A C sin A = A B A C - A B A C 2 ( ) a + b2 Gia s Thnh c www.daythem.edu.vn p (p - a )(p - b)(p - c ) = = Tron : R , r , p l n lt l 1 abc a.ha = b.hb = c.hc = = pr 2 4R n k nh n tr n n o i ti p n k nh n tr n n i ti p v n a chu vi A v B nm v phớa (khỏc phớa) so v i n th n D (ax A + by A + c ) (ax B + by B + c ) < nm v c n ph a so v i n th n D (ax A + by A + c ) (ax B + by B + c ) > v A v B cựng nm tron ng trũn hay cựng nm n oi ng trũn PA / (Cm ) PB / (Cm ) > (x A2 + y A2 - 2ax A - 2by A + c )(x B2 + y B2 - 2ax B - 2by B + c ) > v nm v hai ph a kh c i v i n tr n i m ph a tron m t i m ph a n oi PA / (Cm ) PB / (Cm ) < (x + y - 2ax A - 2by A + c )(x + y - 2ax B - 2by B + c ) < A A B B CH NG I NG DNG O HM KHO ST V V TH CA HM S BI TNH N IU CA HM S C s ý t u n n + Hm s + Hm s t : y = f (x ) n i n tr n K " x 1, x ẻ K v x < x ị f (x ) < f (x ) y = f (x ) n h ch i n tr n K " x 1, x ẻ K v x < x ị f (x ) > f (x ) u n n: Gi s y = f (x ) c o hm tr n kho n I + u y = f (x ) n i n tr n kho n I th f '(x ) 0, " x ẻ I + u y = f (x ) n h ch i n tr n kho n I th f '(x ) Ê 0, " x ẻ I u n : Gi s y = f (x ) c o hm tr n kho n I + u y ' = f '(x ) , " x ẻ I [ f '(x ) = t i s hu h n i m] th y = f (x ) n i n tr n I + u y ' = f '(x ) Ê , " x ẻ I [ f '(x ) = t i s hu h n i m] th y = f (x ) n h ch i n tr n I + u y ' = f '(x ) = , thỡ y = f (x ) kh n i tr n I Chỳ ý: u kho n I c tha i o n ho c n o n thỡ y = f (x ) p ờn t tr n XẫT TNH N IU (t m P n p p + Bc 1: T m t p -y = -y = c nh c a hm s DNG o n t n - Th n m) CA HM S y f x p c c tr n hp sau P (x ) ị T X é : Q (x ) Q (x ) Q ( x ) ị T X é : Q (x ) Gia s Thnh c www.daythem.edu.vn P (x ) ị T X é : Q (x ) > Q (x ) + Bc 2: T m c c i m t i y ' = f '(x ) = ho c y ' = f '(x ) kh n -y = c nh n l t m o hm y ' = f '(x ) Cho y ' = f '(x ) = t m n hi m x i v i (i = 1; 2; n ) + Bc 3: Sp p c c i m th o th t tn n v l p n i n thi n t u y ' = f '(x ) + Bc 4: a vo n i n thi n k t lu n c c kho n n i n v n h ch i n c a hm s - f '(x ) = y ' ị Hm s n i n tn tr n kho n v - f '(x ) = y ' < ị Hm s n h ch i n i m tr n kho n v M t s u ý to n + L u ý i v i hm phõn th c hu t th u = khụng x y + L u ý 2: i v i hm d ng: y = ax + b thỡ hm s lu n ng bi n (ho c ngh ch bi n tr n TX n l lu n cx + d t m c y ' > (ho c y ' < tr n TX ax + bx + c luụn cú ớt nh t hai kho n n i u a 'x + b' i v i hm d ng: y = ax + bx + cx + dx + e luụn cú ớt nh t m t kho n i v i hm d ng: y = ng bi n v m t kho ng ngh ch bi n C ba hm s trờn khụng th luụn n u trờn Ă + L u ý 3: B ng xột d u m t s hm th n p a) Nh thc b c nht: y = f (x ) = ax + b , (a 0) x - tr i ax + b uv ia b a c n uv ia b) Tam thc b c hai : y = f (x ) = ax + bx + c , (a 0) u D < ta c ng xột d u: x c n uv ia f (x ) u D = ta c ng xột d u: x f (x ) c n uD> x -b 2a uv ia c n uv ia i x 1, x l hai n hi m c a tam th c f (x ) = ta c x2 tr i u v i a c n uv ia c) i v i hm m c y ' = f '(x ) = c nhi u n hi m ta t u th o n u n tc Tha i m lõn c n x o g n x n bờn ụ ph i c a b ng xột d u vo f '(x ) [Thay s x o cho d tỡm f (x ) c n x1 ng xột d u: uv ia f '(x ) ] Xột d u theo nguyờn tc: D u c a f '(x ) i du qu n m n v n i du qua nghi m kộp + L u ý X m l i s cỏch gi i ph n tr nh ln i c th ng g p v ta cú th a hm s lng giỏc v d n a th c s tr ng hp +L uý5 ch t nh o hm hm s d n hu t ph n th c Gia s Thnh c www.daythem.edu.vn a b y= c d ax + b ad - cb ị y'= = cx + d (cx + d ) (cx + d ) a y= b a ch nh c x2 + b T ch n ch o ch nh tr t ch n ch o ph ch nh : (Anh b n n ch o hai l n b ch c x+ a' c' a ' b' b' c ' (b ' a - a ' b)x + (c ' a - a ' c )x + (c ' b - b ' c ) ax + bx + c ị y ' = = 2 a 'x2 + b'x + c ' (a ' x + b ' x + c ') (a ' x + b ' x + c ') Bi T m c c kho n n i u c a c c hm s a/ y = - x + 4x - b/ y = x - 6x + 8x + c/ y = x + 4x + d/ y = - x + 6x - 9x + e/ y = x + 3x + 3x + f/ y = g/ y = 2x - x- h/ y = Bi T m c c kho n - x + 2x - x+2 ( d/ y = - 3x ) 6x + Bi T m c c kho n - 2x x+7 c/ y = e/ y = x + - x + 3x + f/ y = x - x+ e/ y = x - 7x - 7x + 15 x + 2x + x - 2x c/ y = 4x - x f/ y = 2x - x + 3x + n i u c a c c hm s sau a/ y = x - sin x , x ẻ ộờ0; p ự ỳ ỷ b/ y = sin x + cos 2x , x ẻ ộờ0; p ự ỳ ỷ c/ y = sin x + cos x , ộờ0; p ự ỳ ỷ d/ y = sin x - cos 2x + sin x + ộ pự ởờ ỳ ỷ f/ y = sin x - e/ y = sin x + cos x + , x ẻ ờ0; ỳ Bi h n minh rn a Hm s y = x + x - cos x - n Hm s y = sin x + tan x - 3x T m u x+2 2 b/ y = - x + - 2x + 5x - a/ y = x + 5x + Bi T m c c kho n x - 8x + b/ y = x- n i u c a c c hm s d/ y = i/ y = n i u c a c c hm s a/ y = 3x + 1- x x - 2x n t i n tr n Ă n ộ ) i n tr n n a kho n ờ0; p m s DNG m s y f x n I C s ý t u t Cho hm s y = f (x , m ) v i m l tham s c t p Hm s y = f (x , m ) n sin x , x ẻ [0; p ] i n tr n c n o n n nh y ' "x ẻ D Tham s m Hm s y = f (x , m ) n h ch i n tr n y ' Ê 0, "x ẻ D Hm s y = f (x , m ) n y ' = f '(x , m ) 0, " x ẻ Ă y ' i n tr n Ă xẻ Ă Hm s y = f (x , m ) n h ch i n tr n Ă y ' = f '(x , m ) Ê 0, " x ẻ Ă max y ' Ê Hm s nh tr n Ă n i n tr n Ă th n ph i c xẻ Ă Gia s Thnh c II P n p www.daythem.edu.vn p D ng 1: N u y ' = f '(x , m ) = ax + bx + c thỡ: ớù a > hm s y = f (x , m ) n i n tn tr n Ă y ' = f '(x , m ) 0; " x ẻ Ă ùỡ ùù D Ê ợ ớù a < hm s y = f (x , m ) n h ch i n i m tr n Ă y ' = f '(x , m ) Ê 0; " x ẻ Ă ùỡ ùù D Ê ợ Chỳ ý: v õ d = ụ x y D ng 2: N u y ' = ax + b ; " x ẻ [a ; b ] thỡ: ùớ y '(a ) ù i n tr n [a ; b ] y ' ; " x ẻ [a ; b ] ỡ hm s y = f (x , m ) n ùù y '( b ) ùợ ùớù y '(a ) Ê hm s y = f (x , m ) n h ch i n tr n [a ; b ] y ' Ê ; " x ẻ [a ; b ] ỡ ùù y '( b ) Ê ùợ D ng 3: N u y ' = f '(x ) = ax + bx + c ho c y ' = f '(x ) l m t hm b t k no khỏc, m ta c n y ' = f '(x ) hay y ' = f '(x ) Ê trờn kho ng (a, b) ho c o n [a, b] (ho c trờn n a o n hay n a kho ng no Th ta lm th o c c c sau: T m mi n c nh c a y ' = f '(x ) c l p t ch m i u th c ch a m kh i i n x v chu n m v m t v t v c n l i l g(x ) u chu n v thnh ph n th c th ph i i u ki n c nh c a i u th c t u g '(x ) ta a vo n t u g '(x ) 3: Tớnh g '(x ) Cho g '(x ) = v t m n hi m p n i n thi n c a g '(x ) t lu n Ln n s n ộ n s ộ l + ta t m g (x ) th a vo n i n thi n ta s l i tr m s n n t tron n i n thi n + ta t m Ê g (x ) th a vo n i n thi n ta s l D ng 4: Tỡm m hm s y = ax + bx + cx + d c Ta gi i nh sau 1: Tớnh y ' = f '(x ) III M t s L uý1 T m i u ki n i n hm s c kho n ( n i n thi n ng bi n (ngh ch bi n) = l ớa ùù D > ợ ) di kho n ù i n v n h ch i n ùỡ n i x - x = l thnh x - x i tr m Ê s n n t tron - 4x 1.x = l (1) (2) S n nh l i t a thnh ph n tr nh th o m Gi i ph n tr nh so v i i u ki n ch n n hi m uý to n ns n thnh th o nh l i t v so s nh n hi m c a ph n tr nh L u ý Ta c th n n to n lo i i i i to n t m tham s m c a m t i u ki n ph n tr nh c n hi m v n hi m ho c n n hi m Bi Tỡm tham s m hm s c hai v i s t ph n tr nh ho c t m Gia s Thnh c www.daythem.edu.vn a/ y = x - 3x + 3(m + 2)x + 3m - n b/ y = x - (2m - 1)x + (2 - m )x + n c/ y = x + (m - 3)x + 2mx + n 2 i n tr n Ă i n tr n Ă i n tr n t p c nh c a n d/ y = - x + 3x + (m - 1)x - 3m - lu n i m (3 - m )x - (m + 3)x + (m + 2)x - lu n tn tr n Ă f/ y = (m - 1)x + (m + 1)x + 3x + lu n n i n tr n Ă e/ y = b/ - Ê m Ê p s: a/ m - e/ - d/ m = Bi Tỡm tham s m c/ m ẻ ộờ6 - 3;6 + 3 ự ỳ Ê m Ê - ỷ f/ m ẻ - Ơ ; - ẩ ộờ2; + Ơ ( ) ) hm s mx + - 2m luụn n h ch i n tr n m i t p c nh c a n x+m mx - b/ y = n i n tr n t n kho n c nh c a n x- m+1 2mx + c/ y = n h ch i n tr n t n kho n c nh c a n x+m a/ y = d/ y = - 2x + (m + 2)x - 3m + x- p s: a/ - < m < n h ch i n tr n t n kho n b/ - < m < c/ - c < m < Bi Tỡm tham s m hm s a/ y = x - 2mx - (m + 1)x + n 3 (- i n tr n kho n 1;1) (0; + Ơ ) x - mx + (2m - 1)x - m + n h ch i n tr n kho n mx + e/ y = n h ch i n tr n kho n (- Ơ ;1) x+m mx + 6x - f/ y = n h ch i n tr n n a kho n ộờ1; + Ơ ) x+2 g/ y = x + m cos x n i n tr n Ă e/ - Ê m Ê Bi Tỡm tham s m ( i n tr n o n ộờ0;2ự ỷỳ d/ y = p s: a/ m Ê - d/ m Ê b/ y = x + 3x + (m + 1)x + 4m n h ch i n tr n kho n c/ y = x + 3x - mx - n nh c a n b/ m Ê - 10 c/ m Ê f/ - < m < - g/ m Ê - (- 2; 0) d/ m 14 h/ - Ê m Ê hm s ) ( ) a/ y = x - m + x - 2m - 3m + x + 2m - m n i n tr n n a kho n ộờ2; + Ơ x (m 1).x (m 4m 3).x m n i n tr n n a kho n ộởờ1; + Ơ ) c/ y x (m 1).x m.(m 2).x n i n tr n o n ộờ4;9ự ỷỳ b/ y 10 ) Gia s Thnh c a h o s t v v th c a hm s cho Tmm ph n tr nh x - 6x + m = c a h os ts S c Bi a c Bi a n i n thi n v v th hm s (C ) th Bi a a vo i n lu n th o m s n hi m c a ph n tr nh x - 8x - m = i t ph n tr nh n th n i qua hai i m c c ti u c a ho hm s y = x + x - 3x + h o s t s i n thi n v v th c a hm s Tmk ph n tr nh 2x + 6x - 18x - k = c i t ph n tr nh ti p tu n c a ho hm s y = h os ts n hi m ph n i t i t ti p tu n vu n c v i n th n y = - x + x - x2 + (C ) 3 i n thi n v v th hm s (C ) i n lu n th o m s n hi m c a ph n tr nh x - 3x + m = i t ph n tr nh ti p tu n c a (C ) i t ti p tu n c h s c ng 3 x + 2x - 3x + (C ) i n thi n v v th hm s (C ) ho hm s y = h os ts a vo (C ) c i n lu n th o tham s m s n hi m c a ph n tr nh (x + 1) - + m - 3x = ho hm s y = x - 8x + 10 (C ) h o s t s i n thi n v v th hm s a vo (C ) c n hi m th c ph n i t ho hm s y = x + 3x - (C ) Bi Bi a www.daythem.edu.vn i n lu n th o m s n hi m c a ph n tr nh x - 6x + 9x + m = i t ph n tr nh ti p tu n c a (C ) t i iao i m c a (C ) v i tr c tun x3 x2 + 2x + (C ) 3 i n thi n v v th hm s (C ) Bi 10 ho hm s y = a h os ts Tmm ph n tr nh 2x + 3x - 12x + m = c n m t n hi m c i t ph n tr nh ti p tu n c a (C ) i t ti p tu n son son v i n th n D : 4x + y - = Bi 11 ho hm s y = f (x ) = 2x - 9x + 12x - (C ) a h os ts i n thi n v v th hm s (C ) Tmm ph n tr nh 2x - 9x + 12x = m c n m t n hi m n c i t ph n tr nh ti p tu n c a (C ) t i i m l n hi m c a ph n tr nh f ''(x ) = Bi 12 ho hm s y = 2x - 6x + (C ) a h os ts i n thi n v v th hm s (C ) a vo (C ) c i n lu n th o m s iao i m c a (C ) v n th n d : y = i t ph n tr nh ti p tu n c a (C ) t i i m c honh n - Bi 13 ho hm s y = 2x - 3x + (C ) a h os ts i n thi n v v th hm s (C ) Tmm ph n tr nh 2x - 3x - m = c a n hi m ph n i t c X c nh t a c c iao i m c a (C ) v n th n y = 2x + 38 m Gia s Thnh c Bi 14 ho hm s y = a c www.daythem.edu.vn x4 - (x - 1) (C ) h o s t s i n thi n v v th hm s a vo i n lu n th o m s n hi m c a ph n tr nh x - 4x - m = i t ph n tr nh ti p tu n c a t i i m A (a;2) ẻ (C ) v i a > x + 2x + (C ) 4 Bi 15 ho hm s y = a c h o s t s i n thi n v v th hm s a vo (C ) t m m ph n tr nh x - 8x + m = c n n hi m th c ph n i t i t ph n tr nh ti p tu n c a (C ) t i iao i m c a (C ) v tr c honh Bi 16 ho hm s y = x + x - (C ) a h os ts i n thi n v v th hm s (C ) Tmm ph n tr nh x + x + m = c hai n hi m th c ph n i t c i t ph n tr nh ti p tu n c a (C ) i t ti p tu n vu n c v i n th n x + 6y - = Bi 17 ho hm s y = 2x - 4x a h os ts (C ) i n thi n v v th hm s (C ) Tmm ph n tr nh x - 2x + m = c a n hi m ph n i t c i t ph n tr nh ti p tu n c a (C ) t i iao i m c a (C ) v i tr c honh l m t s m Bi 18 ho hm s y = a h os ts c honh x4 + 2x - (C ) i n thi n v v th hm s (C ) a vo (C ) t m m c i t iao i m ph n tr nh x - 8x + m = v n hi m i t ph n tr nh ti p tu n c a (C ) t i i m c honh x= - 2 Bi 19 ho hm s y = x - 4x + (C ) a h os ts i n thi n v v th hm s (C ) Tmm ph n tr nh x - 4x + m = c n hi m th c ph n i t c X c nh t a c c iao i m c a (C ) v n th n y = i t ph n tr nh ti p tu n c a (C ) t i c c iao i m Bi 20 ho hm s y = 3x + 2x - (C ) a h os ts i n thi n v v th hm s (C ) c 3x + = m + 2x - i t ph n tr nh ti p tu n c a (C ) t i iao i m c a (C ) v i tr c honh i n lu n th o m s n hi m c a ph n tr nh T m c c i m tr n (C ) c ch u hai tr c t a BI TON GIAO IM CA HAI TH Cho (C ) : y = f (x ), (C ) : y = g(x ) h n tr nh honh iao i m c a (C ) v (C ) l f (x ) = g(x ) 39 (*) Gia s Thnh c www.daythem.edu.vn ct (C ) t i n i m ph n i t ph n tr nh honh n hi m ph n i t iao i m ph n tr nh (*) ] c n (C ) Lu ý 1: u m t tron hai th tr n c n hu t v c TX D = Ă \ {a } hi (C ) ct (C ) t n i m ph n i t ph n tr nh honh iao i m ph n tr nh (*) ] c n n hi m ph n i t a Lu ý 2: nh l c a ax + bx + cx + d = 0, (a 0) u ph n tr nh i t i v i ph n tr nh c a ớù ùù x + x + x = - b ùù a ùù c ỡ x 1x + x 2x + x 3x = ùù a ùù d ùù x 1x 2x = ùùợ a n ax + bx + cx + d = 0, (a 0) c a n hi m ph n Lu ý 3: X m l i ph n ễn t p ph n tr nh i s Lu ý 4: T m tham s th hm s c a n y = f x = ax + bx + cx + d () (C ) ct Ox t i (C ) ct Ox t i p tr ) iao i m ax + bx + cx + d = (C ) ct tr c honh Ox (*) ớù y = f (x ) c c c tr ù i m ph n i t (*) c n hi m ph n i t ỡ ùù yCé yCT < ùợ ớù y = f (x ) c c c tr ù i m ph n i t (*) c n hi m ph n i t ỡ ùù yCé yCT = ùợ l c n th (C ) ti p c v i tr c honh Ox ) (C ) ct Ox t i i m u nh t * ch c (C ) ct Ox t i i m ph n i t c honh () ộ y = f (x ) kh n c c c tr ờ n hi m ờớùù y = f (x ) c c c tr ờỡ ờùù yCé yCT > ởùợ n (*) c n hi m n ph n i t: ớù y = f (x ) ùù c c c tr ùù y y < ùỡ Cé CT ùù xCé > 0, xCT > ùù ùùợ a.f (0) < (hay a.d < 0) (C ) ct Ox t i i m ph n i t c honh m (*) c H c sinh t v h nh i t x 1, x , x th : ị x 12 + x 22 + x 32 = (x + x + x ) - (x 1x + x 2x + x 3x ) t i n i m ph n i t (P n p c ph n tr nh honh ớù y = f (x ) c c c tr ùù ùù y y < ùỡ Cé CT ùù xCé < 0, xCT < ùù ùùợ a.f (0) > (hay a.d > 0) 40 i n hi m m ph n i t: Gia s Thnh c www.daythem.edu.vn Lu ý 5: T m tham s th hm s i m ph n i t l p thnh c p s c n c ch iao i m ax + bx + c = t t = x2 (1) c i m ph n i t ớù D > ùù ph n i t n < t < t ùỡ S > ị tham s ùù ùù P > ợ G i t 1, t l hai n hi m ph n i t c a (2) p th o th t t (1) at + bt + c = (C ) ct tr c honh Ox t i n n sp (2) (1)c () n hi m ph n i t c hai n hi m (3) () c n hi m ph n i t c a l - t2 , - t1 , t1 , t nl n o n hi m n l p thnh c p s c n c ch nh l c honh Ox t i u h n tr nh honh (C ) ct tr n tr n ph n y = ax + bx + c c i t ta t m c tham s So v i ị () u - i tr tham s th a t1 + t = t 9t = t t hp u c u i to n HM S C y = f (x ) = ax + bx + cx + d Bi a ho hm s y = x - 3x + (C ) h os ts i n thi n v v th hm s (C ) G i d l n th n i m ph n i t i qua i m A (3, 20) v c h s cm Tmm n th n d ct (C ) t i a 15 v m 24 ho hm s y = x - 6x + 9x - (C ) S: m > Bi a h os ts i n thi n v v th hm s (C ) G i d l n th n i qua i m A (2,1) v c h s c m T m tham s m n th n d ct th (C ) t i a i m ph n i t S: m > - Bi ho hm s y = x - 3x + a h os ts i n thi n v v th hm s (C ) h n minh rn m i n th n (C ) t i a i m ph n i t I Bi a (C ) i qua i m I (1, 2) v i h s n th i I l trun ho hm s y = x - 2x + (1 - m )x + m h os ts Tm m c k (k > - 3) u ct th hm s i m c a o n th n (1) Tr ch thi H kh i 2010) i n thi n v v th hm s (C ) th hm s (1)ct tr c honh t i i m ph n i t c honh x 12 + x 22 + x 32 < S: < m < 1ĩm Bi Cho (C m ) : y = x - mx - x + m + Tmm 3 x 1, x 2, x v th a m n i u ki n x 12 + x 22 + x 32 > 15 honh 41 (C m ) x 1, x 2, x th a m n i u ki n ct tr c honh t i a i m ph n i t c Gia s Thnh c www.daythem.edu.vn S: m > Bi ho hm s y = x + 2mx + (m - 1)x + c ph n tr nh x + y - = T m c c i tr c a m ( ) i m M (3,1) n th n d c d ct (C ) t i i m A (0, 2), B , C cho th l C m n th n m tam i c M c i n t ch n S: m = - m = ( ) th hm s y = x + 3x + m + x + 2m ct tr c honh t i Bi Tỡm m i m ph n i t c honh m S: < m < (2m th hm s y = x - (m + 1)x - Bi Tỡm m i m ph n i t tron c hai i m c honh ) - 3m + x + 2m (2m - 1) ct tr c honh t i m 1 ĩm 3 ho hm s y = x - 3x (C ) S: < m < Bi a h o s t v v th hm s G i d l n th n qua A 1; - v c h s ( ) c l m i n lu n th o m v tr t n i ia n ( ) th n d v th C Bi 10 ho hm s hm s ctOx t i y = x - 3(m + 1)x + 2(m + 4m + 1)x - 4m (m + 1) (C m ) nh i tr c a m i m ph n i t c honh ul nh n Bi 11 ho hm s y = x - 3mx + 3(m - 1)x - m - a h o s t v v th hm s m = T m m ctOx t i i m ph n i t Bi 12 ho hm s y = x - 3x + a h o s t v v th hm s nh m y = m (x + 1) - ct th t i i m cho ( = 2 v i A - 1; - ) m- x + mx + (3m - 2)x (C m ) a h o s t m = Tmm th (C m ) ctOx t i i m ph n i t Bi 13 ho hm s x3 + 3x (C ) v n th n d : y = m (x - 3) h o s t v v th hm s (C ) Bi 14 ho hm s a y= Tmm y= - (C ) v d c iao i m v i c nh v OA ^ OC , BC = y = x - 3x + 2mx + - 4m (C m ) a h o s t m = (C m ) ctOx t i i m ph n i t c honh T mm 42 Bi 15 ho hm s c T mm (C m ) ctOx t i T mm i m ph n i t c honh (C m ) ct y = mx + t i Bi 16 T m tham s m i m c ch u l n h n - c ch u u th c a c c hm s a/ y = x - 3mx + 6mx - ct tr c honh t i i m ph n i t c honh 42 l p thnh c p s c n Gia s Thnh c www.daythem.edu.vn b/ y = x - 3x - 9x + ; y = 4x + m ct t i c/ y = x d/ y = x c p s nh n i m v i (2m + 4)x + m ct tr c honh t i i m ph n i t c - (m + 1)x - (m - 1)x + 2m - ct tr c honh t i 2 honh ( l trun i mc a l p thnh c p s c n i m ph n i t c honh l p thnh ) e/ y = 3x + m + x + 9mx + 192 ct tr c honh t i i m ph n i t l p thnh c p s nh n Bi 17 T m tham s m c c ph n tr nh sau ch c n n hi m a/ 2x - m + x + 6mx - = b/ x - 3x + - m x + + 3m = ( ) ( ) 1)x + (m - 2)x + - c/ 2x - 3mx + m - x - 3m + 12 = ( e/ 2x + m - Bi 18 T m tham s m d/ x - 6x - c c ph n tr nh sau ch c ( n hi m ) ( ) ( ) ( 8= f/ x - 3m x + 2m = m = a/ x - (m + 1)x - 2m - 3m + x + 2m (2m - 1) = ( ) (m - 4)x + 4m - b/ x - 3m x + 2m = ) ( ) ( ) 3 c/ x - 2m + x + 3m + x - m + = d/ x - 3x + - m x + + 3m = Bi 19 T m tham s m ph n tr nh sau c n hi m ph n i t ( ) ) ( ( ) b/ x - 6x - m - x + 4x - = 2 a/ x - 3mx + m - x - m - = ( ) c/ 2x + m - x + m - x + - m = Bi 20 T m tham s m c c ph n tr nh sau c ( ) (m 2 a/ 2x - 3mx + m - x - c/ d/ n hi m n ph n i t ) ( ( ) ( ) d/ x - mx + 2m + x - m - = c c ph n tr nh sau c ) ( b/ x - 6x - m - x + 4m - = - = x - x + 4x + m + = Bi 21 T m tham s m x - x+m = n hi m m ph n i t ( ) ) ( ) a/ 2x + m - x + m - x + - m = 2 b/ x - 3mx + m - x - m - = c/ x + 3x - 9x + m = d/ x - x + 18mx - 2m = HM S TRNG PH NG y = f (x ) = ax + bx + c Bi a ho hm s y = x h os ts b/ Tỡm m (3m + 2)x + 3m c ( ) th l C m i n thi n v v th hm s m = ( ) n th n y = - ct C m t i i m ph n i t < m < 1, m ho th hm s y = x + (m - 2)x + m - 5m + u c honh S: Bi a h o s t v v th hm s T m tham s m S: < m < Bi a (C ) m = hm s (1) ct tr c honh t i (1) th 5- ( ) ho th hm s y = x + m - x - h os ts i m ph n i t i n thi n v v th hm s (1) (1)khi m 43 = - nh h n Gia s Thnh c T m tham s m Bi a ho hm s www.daythem.edu.vn y = - x + 2mx - 2m + (C ) m = h o s t v v th hm s nh m hm s (C m ) c c nh m (1)t i n th ng y = - ct th hm s i m ph n i t (C m ) c c tr (C m ) ct tr c honh t i i m ph n i t y = x - 2(m + 1)x + 2m (C m ) a h o s t v v th hm s m = (C m ) ct tr c honh t i i m ph n i t nh m Bi ho hm s c nh m Bi a (C m ) ct n th n y = t i ho hm s y = 2mx - x + - 4m h o s t v v th hm s m = i m ph n i t (C m ) b/ nh m hm s (C m ) c c nh m (C m ) ct n th n y = - t i Bi a ho hm s c c tr i m ph n i t y = x + 2(m + 1)x + (C m ) ( ) h o s t v v th hm s C m = nh m (C m ) ct Ox t i i m ph n i t m c honh l p thnh c p s c n c nh m (C m ) ct Ox t i i m ph n i t m c honh u l n h n - Bi a ho hm s y = - x + 2mx - 2m + (C m ) (C ) m = h o s t v v th hm s i n lu n th o m s c c tr c a hm s (C m ) ctOx t i i m ph n i t m c honh c nh m y = x - 10mx + 9m (C m ) a h o s t m = (C m ) ct Ox t i i m ph n i t c honh Tmm Bi l p thnh c p s c n ho hm s c ch y = x - 2mx + 2m - (C m ) a h o s t v v th hm s m = (C m ) c Tmm i m c c tr l p thnh tam i c vu n c n Bi 10 ho hm s c Tmm (C m ) ct Ox t i i m c ch u HM S NHT IN y = f (x ) = Bi a ho hm s y = h os ts x x- (C ) i n thi n v v th hm s (C ) 44 ax + b cx + d u i m c ch u Gia s Thnh c Tmm www.daythem.edu.vn n th n d : y = - x + m ct th (C ) t i hai i m ph n i t S: b / m ẻ (- Ơ , 0) ẩ (4, + Ơ ) Bi a ho hm s y = h os ts - 2x x- (C ) i n thi n v v th hm s (C ) T m m cho tr n th (C ) c hai i m A (x A , y A ), B (x B , y B ) kh c v th a i u ki n ớù mx A - y A = - ù ỡ ùù mx B - y B = - ợ S: m ẻ (- Ơ , - - ) ẩ (- + 5, + Ơ Bi a ho hm s y = h os ts x+2 x+1 ) \ {0} (C ) i n thi n v v th hm s (C ) G i d l n th n i qua i m M (- 1, 3) v c h s cm Tmm d ct (C ) t i hai i m ph n i t Bi T m m n th n y = mx + ct (C ) : y = vu n t i O S: m = Bi cho tam i c 2x - c th (C ) G i D l n th n i qua i m I (2, 0) v c h s x+1 D ct (C ) t i i m ph n i t cho I l trun i m c a o n th n ho hm s y = T m tham s m S: m = Bi 2x + t i hai i m ph n i t x- cm h n minh rn x+ t i hai i m x - m lu n ct th hm s (C ) : y = x+2 n th n d : y = ph n i t T m tham s m n n nh t S: A B = 10 m = - Bi a ho hm s y = h os ts 2x + x+1 i n thi n v v th hm s (C ) T m tham s m n th n y = - 2x + m ct th (C ) t i hai i m ph n i t i cO c i n t ch n S: m = Bi a (C ) v i O l ct a 2x + (C ) x+1 h o s t v v th hm s (C ) ho hm s y= ( ) c l k nh k d ct (C ) t i 1ữ ữ ct (C ) t i ữ 2ữ ứ i m ph n i t G i d l n th n qua A 2;2 c h s Bi a cho tam ho hm s y= 1- x 2x h o s t v v th Tmm (C ) hm s (C ) ổ n th n d : y = m ỗỗx ỗ ỗố 45 i m ph n i t Gia s Thnh c Bi 10 ho hm s a x+1 (C ) (C ) ( ) n th n d : y = x - m ct C t i i m ph n i t (C ) x+1 h o s t v v th hm s (C ) Bi 11 ho hm s M y = 2- x + m lu n ct (C ) t i y = - x + 3x + 9x + (C ) n th n d : y = - Bi 12 ho hm s a y = 1- h o s t v v th hm s Tmm a www.daythem.edu.vn h os ts i m ph n i t (C ) i n thi n v v th hm s ( ) G i A l i m tr n C c x A = v d l n th n qua A c h s c k T mk i m ph n i t x3 - x + (C ) h o s t v v th hm s (C ) Bi 13 ho hm s y = a d : mx - y + + 3m = ct (C ) t i nh m Bi 14 ho hm s a y = - x + mx + - m h o s t v v th hm s nh m (C m ) (C ) m = (C m ) ct tr c honh t i i m ph n i t i m ph n i t Bi 15 ho hm s y = 2x + 3x - mx + m - a h o s t v v th hm s m = (C m ) ct tr c honh t i i m ph n i t nh m Bi 16 ho hm s a h o s t v v th hm s nh k (C ) ct Bi 17 ho hm s a (C ) y = x - (m + 4)x - 4x + m y= (C ) m = n th n y = kx t i i m ph n i t x+ x+1 h o s t v v th hm s ( ) b/ CMR y = 2x + m lu n ct C t i c Tmm MN x+2 (C ) x- a/ CMR d : y = x + m lu n ct (C ) t i Bi 18 ho hm s T mm i m ph n i t M v y= i m v thu c nh nh kh c c a th D OPQ vu n t i O c/ T m m PQ T mm PQ = 14 HM S HU T C 46 ( ) ct C t i Gia s Thnh c www.daythem.edu.vn y = f (x ) = x2 - n th n y = - x + m ct th hm s y = t i hai i m x Bi T m c c i tr c a tham s m ph n i t cho S: m = Bi T m m S: m = = - x + 3x - t i hai i m (x - 1) n th n d : y = m ct (C ) : y = cho = Bi T m tham s m i m ax + bx + c dx + e c honh th hm s (C m ) : y = n mx + x + m ct tr c honh t i hai i m ph n i t v hai x- 1 S: < m< Bi T m tham s m cho trun S: m = Bi ph n n th n y = - 2x + m ct th hm s y = i m c a o n th n h n minh rn i t x2 + x - t i hai i m ph n i t x thu c tr c tun n th n d : y = 3x + m lu n ct th hm s (C ) : y = x + G i I l trun i m c a o n th n t m tham s m t i hai i m x I nm tr n n th n d ' : y = 2x + S: m = x + mx - (C m ) x- a h o s t m = Tmm (d ) : y = m ct (C m ) t i i m Bi ho hm s y= cho OA ^ OB c Tmm (D ) : y = 2x - ct (C m ) t i i m thu c nh nh kh c c a th Tmm (D ) : y = 2x - ct (C m ) t i i m thu c c n m t nh nh c a th BI TON CC I TON KHC LIấN QUAN N TIP TUYN CA TH T m u n n t p n u a) i u ki n c n v hai n C : y = f x v C : y = g x ti p ( ) () ( ) () c l h ph n tr nh ớù f (x ) = g (x ) ù ỡ (*) c n hi m hi m c a h (*) l honh c a ti p i m c a hai n ùù f ' (x ) = g ' (x ) ùợ b) u (C ) : y = px + q v (C ) : y = ax + bx + c th (C ) ti p c v i (C ) ph n ax + bx + c = px + q c n hi m k p Bi T m i u ki n c a tham s m ( ) ( ) c ( ) ( ) & (C ) : tr c honh hai n C v C ti p a/ C : y = x + + m x + mx + 2 47 tr nh Gia s Thnh c ( ) c/ (C ) : y = x d/ (C ) : y = x www.daythem.edu.vn ( ) a/ C : y = x + 2x + & - x4 + x2 - & (C ) : tr c honh & (C ) : y = x + & (C ) : y = x + m (C ) v (C )ti p c (C ) : y = 2mx + m (C ) : y = - x + m & (C ) : y = - x2 + m & (C ) : y = 2x + m & (C ) : y = x & (C ) : y = b/ C : y = x - 2x - m - x + m + m (x + 1) + 3 + 2x + 2x - Bi T m i u ki n c a tham s m ( ) b/ (C ) : y = ( ) hai n x + 2x + 4 ( ) c/ C : y = - 2 ( ) (x - 1) (2m - 1)x - m d/ C : y = x + 2 & 2 2 2 2 ( ) e/ C : y = x- x - x+1 f/ (C ) : y = x- L pp n tr n t p tu n un t a/ G i D : y = ax + b l ti p tu n chun c 2 x2 + m (C ) : y = f (x )v (C ) : y = g (x ) a (C ) v (C ) v i u l honh ti p i m c 2 ( ) honh ti p i m c a D v C ớù f (u ) = au + b ùù ùù f ' u = a () + D ti p c v i (C ) v (C )khi v ch h ùỡ ùù g (v ) = av + b ùù ùù g ' (v ) = a ợ + T (2) v (4) ị f ' (u ) = g ' (v ) ị u = h (v ) (2)vo (1) b = j (u ) + Th (2), (5), (6) vo (3) ị v ị b/ u (C ) v (C )ti p c t i n c a (C ) v (C )t i i m + Th a t tu ( ) a D v C , v l aị uị b T i m c honh (1) (2) c (3) (4) (5) (6) n hi m vi t c ph n tr nh D x o th m t ti p chun c a (C ) v (C )cn l ti p Bi H vi t ph n tr nh ti p tu n chun c a hai th C : y = - x + 5x - 11 a/ C : y = x - 5x + & ( ) b/ (C ) : y = x c/ (C ) : y = x 1 - 5x + & - 5x + & ( ) (C ) : y = - x - x (C ) : y = x + 3x 2 14 10 I TP TNG HP CH NG NG DNG O HM KHO ST V V TH CA HM S mx - 2x + m h n minh rng " m ẻ Ă ho hm s Bi a y= hm s lu n lu n n 48 i n tr n m i kho n c nh c a n Gia s Thnh c www.daythem.edu.vn nh m c nh m n ti m c n ( n c a th i qua i m A - 1; ) n ti m c n n an c a th c ph n tr nh y = - ( ) h o s t v v th C m = ( ) a (C ) t i ( ) i t TTT c a C t i M tr n C c x M = - f i t TTT c ( ) iao i m c a C v i tr c honh c n ( ) TTT c a (C ) i t ti p tu n son son d : y = 6x - TTT c a (C ) i t ti p tu n vu n c D : x + 24y - = TTT c a (C ) i t ti p tu n i qua i m B (- 1; 3) (m + 1)x - 2m + i t TTT c a C c h s h i t i i t j i t ho hm s Bi a nh m y= hm s nh m c nh m x- hm s lu n n h ch i n tr n m i kho n n ti m c n n an c a th i qua A th ct tr c tun t i i m c tun ( c nh ) 3; - n ( ) h o s t v v th C c a hm s m = ( ) a (C ) t i ( ) e/ Vi t TTT c a C t i tr n C c tun f iao i m c a C v i tr c tun i t TTT c ( ) c n ( ) TTT c a (C ) v son son v i n th n d : y = - 2x + TTT c a (C ) v vu n c v i n th n D : x - 8y + = TTT c a (C ) i t ti p tu n i qua i m C (2; 0) i t TTT c a C c h s h i t i i t j i t ho hm s Bi l y= x- x+m- a/ T m m hm s lu n n i n tr n m i kho n c nh b/ T m m n ti m c n n c a th l x = - c/ T m m th ct tr c honh t i i m c honh n - d/ h o s t v v th C m = ( ) Bi ( ) a (C ) t i ( ) e/ i t TTT c a C t i A trờn C c tun f/ i t TTT c g/ i t TTT c a C c h s h/ i t TTT c i/ i t TTT c j/ i t TTT c ho hm s a/ T m a v l ( ) iao i m c a C v i tr c tun c n ( ) a (C ) v son son v i n th n d : y = 3x a (C ) v vu n c v i n th n D : x + 9y a (C ) i t ti p tu n i qua B (3; - 1) y = x + ax + bx + th hm s qua ( ) ( ) i m A 1, v B - 2, - 49 4= Gia s Thnh c b/ ( ) h o s t v v th C v i a = v b = - l - ( ) ( ) d/ i t TTT c a (C ) t i iao i m c a (C ) v i tr c tun e/ i t TTT c a (C ) c h s c n - f/ i t TTT c a (C ) v son son v i n th n d : y = 4x - g/ i t TTT c a (C ) v vu n c v i n th n D : x + 20y = h/ i t TTT c a (C ) i t ti p tu n i qua C (2, 2) ho hm s y = x + (m + 3)x + m - (C ) c/ Bi i t TTT c a C t i i m M trờn C c honh m a/ nh m b/ nh m c/ nh m hm s c i m c c i l x = - n - m ct tr c honh t i i m c honh n m ct tr c tun t i i m c tun (C ) v d/ h o s t v v th hm s e/ i t TTT c a C t i i m A trờn C c tun f/ i t TTT c g/ i t TTT c h/ i t TTT c i/ i t TTT c j/ i t TTT c ho hm s Bi a/ nh m b/ nh m Bi www.daythem.edu.vn i m = n ( ) ( ) a (C ) t i iao i m c a (C ) v i tr c tun a (C ) c h s c n a (C ) v ti p tu n son son v i n th n a (C ) v ti p tu n vu n c v i n th n a (C ) i t ti p tu n i qua C (4, 5) d : y = 9x - D : x - 3y - = x + (m - 1)x + (m + 1)x - (C m ) hm s c i m c c ti u l x = - (C m ) ct tr c honh t i i m c honh n y= - c/ d/ h n minh rn hm s lu n c c c tr h o s t v v th C m = e/ i t TTT c a C t i iao i m c a C v i tr c tun f/ i t TTT c g/ i t TTT c h/ i t TTT c i/ i t TTT c j/ i t TTT c ( ) ho hm s a/ T m m b/ T m m tr t n c/ T m m ( ) ( ) a (C ) t i tr n (C ) c honh n - a (C ) c h s c n a (C ) v ti p tu n son son v i n th n d : y = - 5x + a (C ) v ti p tu n vu n c v i n th n D : x - 12y - = a (C ) i t ti p tu n i qua i m C (- 2, 5) y= x - (m + 2)x + m (C m ) 2 hm s c i m c c tr hm s c i m c c tr l x = - t i l i m c c n (C m ) ct tr c honh t i i m ph n i t ( ) d/ h o s t v v th C m = e/ i t TTT c a C t i M tr n C c honh ( ) ( ) l - 50 i i m c c ti u T m i tr c c Gia s Thnh c www.daythem.edu.vn l n hi m c a ph n tr nh f ''(x ) = ( ) a (C ) v son son v i n th n d : y = - 4x - 10 a (C ) v vu n c v i n th n D : x - 4y = a (C ) i t ti p tu n i qua A (1, 2) f/ i t TTT c a C t i i m c honh g/ i t TTT c h/ i t TTT c i/ i t TTT c ho hm s Bi a/ T m m b/ T m m c/ T m m y = - x + 2mx - 2m + (C m ) hm s c c c tr hm s c i m c c i l x = (C m ) ct tr c honh t i i m ph n i t ( ) d/ h o s t v v th C m = e/ i t TTT c a C t i iao i m c a C v i tr c honh f/ i t TTT c ho hm s Bi ( ) a (C ) t i ( ) i m c honh l n hi m c a ph n tr nh f ''(x ) = - 44 y = x + ax + b x = b/ T m a v b cho y (- 1) = v y '' (- 1) = a/ T m a v b hm s c i tr c c tr c/ h o s t v v th d/ i t TTT c a C t i i m c tun e/ i t TTT c f/ i t TTT c Bi 10 ho hm s a/ a = - v b = n ( ) a (C ) t i i m c honh l n hi m c a ph n tr nh f '' (x ) = a (C ) v son son v i n th n d : y = 3x + y = - x + 3x + 9x + (C ) f ' (x - 1) > t ph n tr nh ( ) a (C ) v c c/ i t TTT c a C t i i m c honh d/ i t TTT c e/ a vo C ( ) b/ h s c k = i qua i mc c y = x + 3x + th (C ) i n lu n s n hi m c a ph n tr nh 2x + 6x - 2m = (d ) : y = k (x + 2) + ct TTT c a (C ) t i i m c honh c/ nh k d/ i t e/ i t ph n tr nh n th n Bi 12 ho hm s i v c c ti u c a th hm s h o s t v v th hm s n i t f ''(x o ) = - o i n lu n s n hi m c a ph n tr nh x - 3x - 9x - + m = i t ph n tr nh n th n Bi 11 ho hm s a/ h o s t v v th hm s b/ Gi i f/ ng y= - th t i i m ph n i t () th a y ' x = i qua i m c c i v i m c c ti u x + (m - 1)x + (m + 3)x - (C m ) a/ T m m hm s n i n tr n t p b/ h o s t v v C v i m = c nh ( ) c/ a vo th i n lu n s n hi m c a ph n tr nh 2x + 6x + 18x + 24 + 3k = 51 Gia s Thnh c d/ e/ www.daythem.edu.vn i t ph n tr nh n th n i qua i m c c i v i m c c ti u i t TTT c a C t i i m c honh th a y ''(x ) = - ( ) (d ) : y = a (x + 3) - 13 ct (C ) t i f/ T m a Bi 13 ho hm s y= c/ d/ hm s c c c ti u n - a vo th ( ) y= i n lu n s n hi m c a ph n tr nh x - 6x + = m i t TTT c a C t i i m c honh Bi 14 ho hm s a/ b/ x + ax + b x = h o s t v v (C ) a = - v a = - a/ T m a v b b/ i m ph n i t ( ) th a y '' x o = 18 x - 2x 4 h o s t v v th c a hm s i t TTT c a C t i c c iao i m c a C v i tr c honh ( ) ( ) (C ) ct ara ol (P ) : y = - 2x t i i m ph n i t TTT c a (C ) t i i m c honh l n hi m c a ph n tr nh c/ nh m d/ i t e/ i n lu n th o k s n hi m c a ph n tr nh x - 8x - - 4k = Bi 15 ho hm s y = - x + (m + 1)x - 2m - (C m ) a/ nh m hm s b/ nh m hm s c/ nh m hm s d/ h o s t v v C e/ f/ i t TTT c n y ''(x ) = th ct tr c honh t i i m ph n i t c c c tr c c c i x = ( ) m = a (C ) t i c c iao ( ) i m c a C v i n th n y = - i t honh i n lu n s n hi m c a ph n tr nh x - 4x + m = 52 c a n l s m ... 2 ;1 ỳ ỷ a/ y = f x = x - 3x + tr n o n ộờ- 10 ;10 ự ỳ ỷ () ớù f (x ) = f (1) = f (2) = ùù ù ộ- 10 ;10 ựỷỳ p s: a/ ùỡ ởờ ùù max f (x ) = f (- 10 ) = 13 2 ùù ộ- 10 ;10 ự ỳ ỷ ợù ởờ ớù max f (x ) = 19 ... ùợ ờở ỳỷ ớù max y = 10 ùù ộ ự ùù ờờ- 10 ; 10 ỳỳ ỷ d/ ỡ ùù y = - 10 ùù ộờ- 10 ; 10 ựỳ ỳ ùùợ ờở ỷ ớù max y = x = ùù ộ ự - 1; 3ỷỳ f/ ùỡ ởờ ùù y = x = ùùợ ộởờ- 1; 3ựỷỳ x = x = - 10 1, x = c a c c hm s... 2)x - m (m - 1) Bi 3 2 ho hm s : y = x + (m - 1) x + (m - 4m + 1) x - (m + 1) T m m 1 + = (x + x ) x1 x 2 p s m = ho c m = 1 Bi ho hm s : y = mx - (m - 1) x + (m - 2)x + Tm m 3 x 1; x n th i hai