HÀM số 747 bài tập TRẮC NGHIỆM cực TRỊ hàm số file word

HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD 747 BI TP TRC NGHIM CC TR HM S BIấN SON V SU TM HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD Thy Phan Ngc Chin Cõu 1: Giỏ tr cc i ca hm s y = x 3x + l A D C B Cõu 2: im cc i ca th hm s y = x 3x l: A ( 0; ) B ( 2; ) C ( 1; 3) D ( 1; ) Cõu : imccicathhms y = x x + x l: 3 ; B ữ ữ A ( 1;0 ) Cõu 4: Hm s y = A x = 3 ; D + ữ ữ C ( 0;1) x 3x + t cc i ti: x2 B x = C x = D x = Cõu 5: Hm s: y = x + 3x + t cc tiu ti x bng A -1 Cõu 6: Hm s: A B y= C - D x 2x2 t cc i ti x bng B C D Cõu 7: Hm s y = x3 3x + 3x cú bao nhiờu cc tr? A B C.0 D HTTP://DETHITHPT.COM HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD x3 y = x2 + 3x + 3 To im cc i ca th hm s l Cõu 8: Cho hm s A (-1;2) 3; ữ C B (1;2) Cõu 9: Hm s y = x D (1;-2) x + cú A.Mt c i v hai cc tiu B Mt cc tiu v hai cc i C Mt cc i nht D Mt cc tiu nht Cõu 10: Giỏ tr cc i ca hm s y = x 3x A + B 2 3x + bng C + D Cõu 11: Tỡm m hm s y = mx + x + 12 x + t cc i ti x = A m = Cõu 12: Cho hm s y = B m = C m = D m = x4 + x x + Gi x1 , x2 l hai nghim ca phng trỡnh y ' = Khi ú, x1 + x2 bng: A B C D Cõu 13: Tỡm m hm s y = x ( m + 1) x cú ba cc tr A m B m > C m > D m > 2 Cõu 14: Tỡm m hm s y = x ( m + 1) x + ( m + m ) x cú cc i v cc tiu A m > B m > C m > D m > Biờn son v su tm Cõu 15: Gi y1 , y2 ln lt l giỏ tr cc i v giỏ tr cc tiu ca hm s y = x + 10 x Khi ú, y1 y2 bng: A C 25 B D Cõu 16:Hm s y = x x + mx t cc tiu ti x = khi: A m = B m C m > D m < VD1 y = x3 + mx2 + ( 2m 1) x Cõu 17: Cho hm s Mnh no sau õy l sai? A m thỡ hm s cú cc i v cc tiu; B m < thỡ hm s cú hai im cc tr; C m > thỡ hm s cú cc tr; D Hm s luụn cú cc i v cc tiu Cõu 18: Cho hms y=x3-3x2+1 Tớch cỏc giỏ tr cc i v cc tiu ca th hm s bng A -6 B -3 C D 3 Cõu 19:Hms y = x mx + cú cctr : A m > B m B m < C m = D m Cõu 37 Tỡm m hm s y = x3 - mx2 + 3x - t cc tiu ti x = A m = - 15 B m = 15 C m = - 15 D m = 15 Cõu 38 Vi giỏ tr no ca m thỡ hm s y = x3 + mx2 + 3x + 2m - cú cc i v cc tiu? ( ) A m ẻ - 3;3 C m ẻ B m ẻ ( - Ơ ;- 3) ẩ ( 3; +Ơ ) ( ộ- 3;3ự ỳ ỷ D m ẻ - Ơ ;- ộ3; +Ơ 3ự ỳ ỷẩ ) Cõu 39 Tỡm m hm s y = x3 - 3x2 + mx - cú im cc tr x1, x2 tha x12 + x22 = A m = B m = C m = D m = - Cõu 40 Vi giỏ tr no ca m thỡ hm s y = x2 - 2(m + 1)x + m cú cc tr trờn khong (0;1)? A - < m < B < m < C - < m < - D - < m < Biờn son v su tm Thy Nguyn Vit Thụng Cõu 41 S im cc tr ca th hm s y = x + x l: A B C D Cõu 42 Cho hm s y = x + 3x Tng cỏc giỏ tr cc tr ca hm s l: A -9 B C -1 Cõu 43 S cỏc im cc tr ca hm s y = ( x ) A B D -5 ( x + 1) C l: D Cõu 44 Cho hm s y = x x Trong cỏc im sau, im no cú ta sau õy l im cc tr ca hm s ó cho A ( 1; ) B ( 3;0 ) C ( 1;0 ) ( D 2; ) Cõu 45 im cc tr ca th hm s y = x x cú ta l: A ( 1; ) ( B 0; ) C ( 1;0 ) D ( 3;0 ) Cõu 46 Giỏ tr ca m hm s y = ( m ) x mx + khụng cú cc tr l: m A m B m m C m > D m Cõu 47 Hm s y = x + x + cú s im cc tr l: A B C D 3 2 Cõu 48 Hm s y = x 3mx + ( m m ) x 2m cú hai im cc tr khi: A m > B m C m > D m tựy ý HTTP://DETHITHPT.COM HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD Cõu 49 Hm s y = A m > x mx + 2m + cú hai im cc tr khi: 2x B m Cõu 50 th hm s y = x + + C m < D m tựy ý cú hai im cc tr nm trờn ng thng y = ax + b thỡ tớch a.b x bng: A B C Cõu 51 Cho hm s y = A D -2 x2 x + Khong cỏch gia hai im cc tr l: x +1 B C D Cõu 52 Cho hm s y = x x Tỡm mnh ỳng cỏc mnh sau: A Giỏ tr cc i bng B im cc tiu cú ta l ; 1ữ 1 C im cc tiu l ; ữ D Hm s khụng cú cc tr Cõu 53 Trong cỏc ng thng sau, ng thng no i qua hai im cc tr ca hm s y = x3 + 3x + x A y = x B y = 1 x+ 3 C y = x 10 D x y 10 = Cõu 54 Hm s y = x ( m 1) x + t cc tiu ti im x = khi: A m = 13 B m < 13 C m > D m Cõu 55 iu kin ca m hm s y = x3 3x + 3mx m + cú cc tr l: A m < B m C m > D m Biờn son v su tm Cõu 56 Hm s y = A m = hoc m = x mx + ( m2 m + 1) x + t cc i ti im x = khi: B m = C m = D m tựy ý Cõu 57 Hm s y = x + ( m ) x + m t cc i ti im x = thỡ: A m = B m = C m < D m > Cõu 58 S cc tr ca hm s y = x x + A B C D Cõu 59 Vi m bng bao nhiờu thỡ th hm s y = x + 2mx m cú hai cc tr thng hng vi gc ta A m = C m = B m = 3 D m Cõu 60 Cho hm s y = cos x + , x ( ;0 ) thỡ khng nh no sau õy sai: A Hm s t cc tiu ti im x = C Ti x = 12 hm s khụng t cc i B Hm s t cc i ti im x = D Ti x = 11 12 hm s khụng t cc tiu 12 Khụng bit ca thnh ca mỡnh :D Cõu 61 im cc i ca hm s y = - x3 + 3x + cú honh l: A -3 B -2 C -1 D C D Cõu 62 Hm s: y = x3 + x + t cc tiu ti: A -1 B HTTP://DETHITHPT.COM 10 HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD C (C) cú im un D (C) cú tõm i xng Cõu 671: Cho hm s: y =(1 - m) x - mx +2m - Tỡm m th hm s cú ỳng mt cc tr A m Ê m B m 1 C m < D m > Cõu 672: th hm s: y =x +x - cú bao nhiờu cc tr: A B C D Cõu 673: Cho th (C): y =x - x +1 Vit phng trỡnh tip tuyn vi (C) ti im cc i A x = B x = C y = D y = Cõu 674: Cho th (C): y =x - x +1 Vit ph.trỡnh ng thng i qua im cc tiu ca (C) A x = B y =- D x =- C y = Cõu 675: Vi giỏ tr no ca m thỡ hm s sau cú cc tr: y = x +mx - mx - A m B - Cho hm s y = x3 3x2 mx + (m l tham s) cú th l (Cm) Xỏc nh m (Cm) cú cỏc im cc i v cc tiu cỏch u ng thng y = x Cõu A m = B m = D m= C m = Cho hm s y = x3 3mx2 + 4m3 (m l tham s) cú th l (Cm) Xỏc nh m (Cm) cú cỏc im cc i v cc tiu i xng qua ng thng y = x Cõu A m= 2 B m = C m = D m = Cho hm s y = x3 + 3mx2 3m Vi giỏ tr no ca m thỡ th hm s cú im cc i v im cc tiu i xng vi qua ng thng d: x + 8y 74 = Cõu A m= B m = C m = D m = Cho hm s y = x3 3x2 + mx (1) Vi giỏ tr no ca m thỡ th hm s (1) cú cỏc im cc i v im cc tiu i xng vi qua ng thng d: x 2y = Cõu A m = B m = C m = D m = Cho hm s y = x3 3(m+ 1)x2 + 9x + m (1) cú th l (Cm) Vi giỏ tr no ca m thỡ th hm s cú im cc i v im cc tiu i xng vi qua Cõu ng thng d: y = x HTTP://DETHITHPT.COM 102 HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD A m = B m = C m = D m= Cõu 10 Cho hm s y = x3 3(m+ 1)x2 + 9x m, vi m l tham s thc Xỏc nh m hm s ó cho t cc tr ti x1, x2 cho x1 x2 m > 1+ m < A B m C m< v 1+ < m D m = Cõu 11 Cho hm s y = x3 + (1 2m)x2 + (2 m)x + m+ , vi m l tham s thc Xỏc nh m hm s ó cho t cc tr ti x1, x2 cho x1 x2 > m> A m < B m > 3+ 29 29 3+ 29 C m> m< m< 8 D m = Cõu 12 Cho hm s y = x3 mx2 + mx 1, vi m l tham s thc Xỏc nh m hm s ó cho t cc tr ti x1, x2 cho x1 x2 65 m A 1+ 65 m B m = C 65 1+ 65 m 2 D m < 1 Cõu 13 Cho hm s y = x3 (m 1)x2 + 3(m 2)x + , vi m l tham s thc 3 m Xỏc nh hm s ó cho t cc tr ti x1, x2 cho x1 + 2x2 = A m = 34 B m = C m = 34 D m = 34 Biờn son v su tm 103 Cõu 14 Cho hm s y = 4x3 + mx2 3x Tỡm m hm s cú hai im cc tr x1, x2 tha x1 = 4x2 A m = B m = C m = D m = x ax2 3ax + (1) (a l tham s) Tỡm a hm s (1) t cc tr ti x1, x2 phõn bit v tho iu kin: Cõu 15 Cho hm s y = x12 + 2ax2 + 9a a2 + a2 x22 + 2ax1 + 9a =2 A a = B a = C a = 2 Cõu 16 Cho hm s y = 2x + 9mx + 12m x + (m l tham s) D a = Tỡm cỏc giỏ tr ca m hm s cú cc i ti xC, cc tiu ti xCT tha món: x2Cẹ = xCT A m = B m= C m = D m = Cõu 17 Cho hm s y = (m+ 2)x3 + 3x2 + mx , m l tham s Tỡm cỏc giỏ tr ca m cỏc im cc i, cc tiu ca th hm s ó cho cú honh l cỏc s dng A < m < B < m < Cõu 18 Cho hm s y = x mx + (m2 3)x 14 A m = B m = C < m < D < m < (1), m l tham s C m = 14 D m = 14 HTTP://DETHITHPT.COM 104 HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD Cõu 19 Cho hm s y = x3 + (1 2m)x2 + (2 m)x + m+ (m l tham s) (1) Tỡm cỏc giỏ tr ca m th hm s (1) cú im cc i, im cc tiu, ng thi honh ca im cc tiu nh hn A < m< Cõu 20 Cho hm s y = B < m< C < m< m x + (m 2)x2 + (m 1)x + D < m< (Cm) Tỡm m hm s cú cc i ti x1, cc tiu ti x2 tha x1 < x2 < A < m< B < m< C < m< D < m< 3 Cõu 21 Cho hm s y = x + (1 2m) x + (2 m) x + m + (Cm) Tỡm m hm s cú ớt nht im cc tr cú honh thuc khong (2;0) A 10 < m < B m Cõu 22 Cho hm s y = x3 3x2 + C m < D m ; 1ữ 2;+ ) (1) Tỡm im M thuc ng thng d: y = 3x tng khong cỏch t M ti hai im cc tr nh nht A M ; ữ B M ; ữ C M ; ữ D M ; ữ 5 5 5 Cõu 23 Cho hm s y = x3 3mx2 + 3(m2 1)x m3 + m (1) Tỡm m hm s (1) cú cc tr ng thi khong cỏch t im cc i ca th hm s n gc ta O bng ln khong cỏch t im cc tiu ca th hm s n gc ta O A m = m = 2 m = 3+ 2 B m = + 2 m = 2 C m = + 2 m = 2 D Cõu 24 Cho hm s y = x3 3x2 mx + cú th l (Cm) Tỡm m (Cm) cú cỏc im cc i, cc tiu v ng thng i qua cỏc im cc tr song song vi Biờn son v su tm 105 ng thng d: y = 4x + A m = B m = C m = D m = Cõu 25 Cho hm s y = x3 + mx2 + 7x + cú th l (Cm) Tỡm m (Cm) cú cỏc im cc i, cc tiu v ng thng i qua cỏc im cc tr vuụng gúc vi ng thng d: y = 3x A m = 10 B m = 10 C m= 10 D m = 10 Cõu 26 Cho hm s y = x3 3x2 mx + cú th l (Cm) Tỡm m (Cm) cú cỏc im cc i, cc tiu v ng thng i qua cỏc im cc tr to vi ng thng d: x + 4y = mt gúc a = 450 15 B m= A m= 39 m = 10 C m = D m = 39 10 Cõu 27 Cho hm s y = x3 3x2 + (C) Tỡm m ng thng i qua hai im cc tr ca (C) tip xỳc vi ng trũn (S) cú phng trỡnh (x m)2 + (y m 1)2 = A m = 2; m = B m = Cõu 28 Cho hm s y = x3 3mx + C m = D m = (Cm) Tỡm m ng thng i qua im cc i, cc tiu ca ( Cm) ct ng trũn tõm I (1;1) , bỏn kớnh bng ti hai im phõn bit A, B cho din tớch IAB t giỏ tr ln nht A m = 3 B m = C m = D m = Cõu 29 Cho hm s y = x3 + 6mx2 + 9x + 2m (1), vi m l tham s thc HTTP://DETHITHPT.COM 106 HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD Tỡm m th hm s (1) cú hai im cc tr cho khong cỏch t gc to O n ng thng i qua hai im cc tr bng A m = 37 B m= C m = D m = Cõu 30 Cho hm s y = x3 3x2 + (m 6)x + m (1), vi m l tham s thc Tỡm m th hm s (1) cú hai im cc tr cho khong cỏch t im A(1; 4) n ng thng i qua hai im cc tr bng m = A m = 1053 12 12 265 m = B m = 1053 24 m = C m = 1053 249 m= D m= 1053 249 Cõu 31 Cho hm s y = x3 3x2 + mx + (1), vi m l tham s thc 11 ữ n ng Tỡm m th hm s (1) cú hai im cc tr cho khong cỏch t im I ; thng i qua hai im cc tr l ln nht A m = B m = C m= D m = Cõu 32 Cho hm s y = 2x2 3(m+ 1)x2 + 6mx + m3 Tỡm m th hm s cú hai im cc tr A, B cho AB = A m = B m= 0; m= C m = D m = Cõu 33 Cho hm s y = x3 3mx2 + 3(m2 1)x m3 + 4m (1) Tỡm m th ca hm s (1) cú hai im cc tr A, B cho OAB vuụng ti O m = A m = m = B m = m = C m = m = D m = Biờn son v su tm 107 Cõu 34 Cho hm s y = 2x2 3(m+ 1)x2 + 6mx + m3 (1) Tỡm m th ca hm s (1) cú hai im cc tr A, B cho tam giỏc ABC vuụng ti C, vi C(4;0) A m= B m = Cõu 35 Cho hm s y = x3 + 3x2 + m C m = D m = (1) Xỏc nh m th ca hm s (1) cú hai im cc tr A, B cho AOB = 1200 A m = 12 B m = 12 3 C m = 12 + 3 D m = 12 + 3 Cõu 36 Cho hm s y = x3 3x2 + m2 m+ (1) Tỡm m th hm s (1) cú hai im cc i, cc tiu l A v B cho din tớch tam giỏc ABC bng 7, vi im C(2; ) m = A m = m = B m = m = C m = m = D m = Cõu 37 Cho hm s y = x3 3(m+ 1)x2 + 12mx 3m+ (C) Tỡm m hm s cú hai cc tr l A v B cho hai im ny cựng vi im C 1; ữlp thnh tam giỏc nhn gc ta O lm trng tõm A m = B m = C m = D m = Cõu 38 Cho hm s y = f (x) = 2x3 + 3(m 3)x2 + 11 3m ( Cm) Tỡm m (Cm) cú hai im cc tr M1, M2 cho cỏc im M1, M2 v B(0; 1) thng hng A m = B m = C m = D m= HTTP://DETHITHPT.COM 108 HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD x mx2 + (m2 1)x + (Cm) Tỡm m hm s cú cc i, cc tiu v yCẹ + yCT > Cõu 39 Cho hm s y = A 1< m < m > B m > C < m < Cõu 40 Cho hm s y = x3 (m+ 1)x2 + (m+ 1)3 3 D m < (1) (m l tham s thc) Tỡm m cỏc im cc i v cc tiu ca th (1) nm v phớa (phớa v phớa ngoi) ca ng trũn cú phng trỡnh (C): x2 + y2 4x + = A m B < m < 2 C m < D < m< Cõu 41 Cho hm s y = x3 mx2 x + m+ (Cm) Tỡm m th (Cm) cú im cc tr v khong cỏch gia im cc tr l nh nht B m= A m = C m = D m = 12 Cõu 42 Cho hm s y = x3 3x2 mx + (1) Tỡm m hm s (1) cú cc tr v ng thng i qua im cc tr ca th hm s to vi hai trc to mt tam giỏc cõn A m= B m = C m = D m = x mx2 + (m2 m+ 1)x + (1) Tỡm m hm s cú cc tr khong (;1) Cõu 43 Cho hm s : y = A 1< m < B m < C m = D m > Biờn son v su tm 109 x mx2 + (m2 m+ 1)x + (1) Tỡm m hm s cú cc tr khong (1; +) Cõu 44 Cho hm s : y = A m < C m> B m > D m < x mx2 + (m2 m+ 1)x + (1) Tỡm m hm s cú hai cc tr x1, x2 tho x1 < 1< x2 Cõu 45 Cho hm s : y = A 1< m< B m < C 1< m m > D m < 1 x mx2 + (m2 m+ 1)x + (1) Tỡm m hm s cú hai cc tr x1, x2 tho x1 < x2 < Cõu 46 Cho hm s : y = A m < C m > B m D 1< m < 3 x mx2 + (m2 m+ 1)x + (1) Tỡm m hm s cú hai cc tr x1, x2 tho 1< x1 < x2 Cõu 47 Cho hm s : y = A m< C m> B m < D m > Cõu 48 Cho hm s y = x4 2(m2 m+ 1)x2 + m Tỡm m th (C) cú khong cỏch gia hai im cc tiu ngn nht A m = Cõu 49 Cho hm s y = B m = x mx2 + 2 C m = D m = (1) HTTP://DETHITHPT.COM 110 HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD Xỏc nh m th ca hm s (1) cú cc tiu m khụng cú cc i A m> C m B m < Cõu 50 Cho hm s y = x4 + 2mx2 D m (Cm) Tỡm cỏc giỏ tr ca m tt c cỏc im cc tr ca (Cm) u nm trờn cỏc trc to A m B m= C m > D m 0, m = Cõu 51 Cho hm s y = x4 + (3m+ 1)x2 (vi m l tham s) Tỡm tt c cỏc giỏ tr ca m th hm s cú ba im cc tr to thnh mt tam giỏc cõn cho di cnh ỏy bng ln di cnh bờn 4 2 Cõu 52 Cho hm s y = f (x) = x + 2(m 2)x + m 5m+ (Cm) A m = B m = C m = D m = Tỡm cỏc giỏ tr ca m th (Cm) ca hm s cú cỏc im cc i, cc tiu to thnh tam giỏc vuụng cõn A m = B m = C m = Cõu 53 Cho hm s y = x4 + 2(m 2)x2 + m2 5m+ D m = ( Cm) Vi nhng giỏ tr no ca m thỡ th (Cm) cú im cc i v im cc tiu, ng thi cỏc im cc i v im cc tiu lp thnh mt tam giỏc u A m= 3 B m= 1+ 3 C m = 3 D m= 3 Cho hm s y = x4 2mx2 + 2m+ m4 cú th (Cm) Vi nhng giỏ tr no ca m thỡ th (Cm) cú ba im cc tr, ng thi ba im cc tr ú lp thnh mt tam giỏc cú din tớch S = Cõu 54 Biờn son v su tm 111 A m= 16 B m= 1+ 3 C m = + 16 D m= 3 Cõu 55 Cho hm s y = x4 + 2mx2 + m2 + m cú th (Cm) Vi nhng giỏ tr no ca m thỡ th (Cm) cú ba im cc tr, ng thi ba im cc tr ú lp thnh mt tam giỏc cú mt gúc bng 1200 A m= C m = B m = 3 D m= 3 Cõu 56 Cho hm s y = x4 2mx2 + m cú th (Cm) Vi nhng giỏ tr no ca m thỡ th (C m) cú ba im cc tr, ng thi ba im cc tr ú lp thnh mt tam giỏc cú bỏn kớnh ng trũn ngoi tip bng A m = 2, m = 1+ B m = 1, m = 1+ 1+ C m = 0, m = D m= 1, m= 2 Cõu 57 Cho hm s y = x4 2mx2 + (Cm) Tỡm cỏc giỏ tr ca m (Cm) cú im cc tr to thnh mt tam giỏc cú ng trũn ngoi tip i 5 qua im D ; ữ A m = B m= C m = D m = Cõu 58 Cho hm s y = x4 2(1 m2)x2 + m+ (Cm) Tỡm m th (Cm) cú im cc tr to thnh mt tam giỏc cú din tớch ln nht A m = Cõu 59 Cho hm s y = B m = C m = D m = 1 x (3m+ 1)x2 + 2(m+ 1) (Cm) Tỡm m th (Cm) cú im cc tr to thnh mt tam giỏc cú trng tõm l gc to O HTTP://DETHITHPT.COM 112 HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD A m = ; m = 3 B m= C m = D m = Chỳc cỏc bn hc tt Tng ti liu gũm cú 747 cõu cc tr.c tụi su tm v biờn son Biờn son v su tm 113 ... nhiờu cc tr? A B C.0 D HTTP://DETHITHPT.COM HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD x3 y = x2 + 3x + 3 To im cc i ca th hm s l Cõu 8: Cho hm s A (-1;2) 3; ữ C B (1;2)... xCT = Thy Nguyn Vit Dng HTTP://DETHITHPT.COM HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD Cõu 21 S im cc tr ca hm s y = A.1 x3 - x + l: B C D Cõu 22 Hm s y = x3 - 3x2 - 9x - cú im... ta B x = - C x = D x = HTTP://DETHITHPT.COM HTTP://DETHITHPT.COM WEBSITE CHUYấN THI TI LIU FILE WORD Cõu 34 Hm s y = x3 - 2x2 + 3x - t cc tiu ti A x = B x = C x = - Cõu 35 Tip tuyn ti im cc