TÀI LIỆU TÍNH ĐƠN ĐIỆU CỦA HÀM SỐ

www.tuhoc.edu.vn y f(x2) f(x1) (a ; b) x (a ; b): x1 < x2 f(x1) < f(x2) a x1 O x2 b x y (a ; b) x (a ; b): x1 < x2 f(x1) > f(x2) f(x1) f(x2) x f (x) x (a ; b) f(x) f (x) x (a ; b) f(x) f (x) x (a ; b) f(x) x f (x) f(x) a b + x2 b a x1 O (a ; b) x f (x) a b – f(x) htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn – : Tính f (x) – (f (xi ) i 0) – i – VD1: x y x 2x = HD – Ta có: y x2 x 2, y x y y x x 2 –1 + 19 – + ( ; 1) (2; ), htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn VD2: x x y = HD x (x 1)2 – Ta có: y \ {–1} x x \ {–1} –1 y + + y ( ; 1) ( 1; ) htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn (a) y = –x3 + x2 – 5; (b) y = x4 – 2x2 + (a) y x x ; (b) y y x x y x ( x ; 1) (1; 2x ) x2 htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn – – cho TOPPER Chú ý VD3 = HD x = y không xác – Ta có: y [0 ; 3] x2 y x x2 x (0 ; 3) (1) VD4: y x x2 [2; 2] = HD D – Ta có: y 2x x2 [ 2 ; 2] x (2 ; 2) (1) [2; 2] (2) [2; 2] htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn y 2x x2 y x2 y [3; ) x x (0 ; 2] 0; f(x) 0; sin2 x cos x ; htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn TOPPER Chú ý y (a + bx + c 0) ta có: f(x) f(x) x x a 0, y VD5: a = x 0, K x K + (3 – m)x2 – (2m – 1) + – Ta có: y 3x2 2(3 m)x (2m 1) y' ' g m2 12m 12 6 m VD6 g(x) 6 ' g x m 6 6 y mx 10m x m = \ {–m} – Ta có: y m2 10m (x m)2 Do (x + m)2 > 0, x y D y g(m) = m2 – 10m + > – 10m + 0, m m x htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn y y A y x mx mx x m 1 x 4x (m 1)x2 (m 3)x (0 ; 3) htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn [a ; b] ta – – h(x) > x VD7: x [a ; b] (0; ) = HD (0; ) Ta có: h (x) g (x) 0, cos2 x x 1, (0; ) (0; ) nên cos2 x (0; ) htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn B 0; C D tan x f(x) x x x3 tan x, x 0; 0; 4 x, x 0; 0; tan x 2 htttp://tuhoc.edu.vn/blog 10 www.tuhoc.edu.vn TOPPER Chú ý 0) =0 x = x0 VD8: trình, nhiên x 4x 13 = x f(x) Ta có: f (x) x 4x x 13 4x 1 x ; E F G x x5 x3 x2 x3 3x 3x 15 3x 4x 0 x2 htttp://tuhoc.edu.vn/blog 11 www.tuhoc.edu.vn (0; ), ( (1; ( ; 0), ( ; ) ) ; 1) , (0 ; 1) ( (2; (1; ) ) 0; f (x) ; 0) (0 ; 1), cos2 x tan2 x x 0; 2 0; [0; ] , f (x) x 0; 8m ; [–2 ; 2] A y < < < x2 af(0) af(3) 1, y x2 m ) 12 B 0; htttp://tuhoc.edu.vn/blog Ex=2 F x = –1 Gx=1 12 [...]... www.tuhoc.edu.vn 2 (0; ), 3 1 ( (1; ( 2 ; 0), ( ; 3 ) ) ; 1) , (0 ; 1) 2 ( (2; (1; ) ) 6 0; f (x) ; 0) và (0 ; 1), 1 cos2 x tan2 x 1 0 x 0; 2 2 0; 7 [0; ] , f (x) 0 x 2 3 0; 3 8m ; 3 [–2 ; 2] A y 1 < 0 < 3 < x2 0 af(0) 0 af(3) 0 1, 0 y x2 m 0 ) 12 7 B 0; htttp://tuhoc.edu.vn/blog 2 Ex=2 F x = –1 Gx=1 12  ... m) x2 – ( 2m – 1) + – Ta có: y 3x2 2(3 m) x ( 2m 1) y' ' g m2 1 2m 12 6 m VD6 g(x) 6 ' g x m 6 6 y mx 1 0m x m = { m} – Ta có: y m2 1 0m (x m) 2 Do (x + m) 2 > 0, x y D y g (m) = m2 – 1 0m + > – 1 0m. .. (x + m) 2 > 0, x y D y g (m) = m2 – 1 0m + > – 1 0m + 0, m m x htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn y y A y x mx mx x m 1 x 4x (m 1)x2 (m 3)x (0 ; 3) htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn... ) ) 0; f (x) ; 0) (0 ; 1), cos2 x tan2 x x 0; 2 0; [0; ] , f (x) x 0; 8m ; [–2 ; 2] A y < < < x2 af(0) af(3) 1, y x2 m ) 12 B 0; htttp://tuhoc.edu.vn/blog Ex=2 F x = –1 Gx=1 12