extreme f(x)= 1/4 e^x+e^{-x}

解答

极值点

f (x) = \frac{1}{4} e^{x} + e^{- x}

极小值 (ln (2), 1)

求解步骤

f^{'} (x) = \frac{1}{4} e^{x} - e^{- x}

Find intervals:

递减

: - \infty < x < ln (2),

递增

: ln (2) < x < \infty

将

x = ln (2)

代入

\frac{1}{4} e^{x} + e^{- x} : 1

极小值 (ln (2), 1)

e x t re m e f (x) = \frac{5 x}{x ^{2} + 16}, 0 \leq x \leq 12

e x t re m e sin^{2} (x) - cos (x)

e x t re m e P (x, y) = 0.3 x^{2} + 0.2 y^{2} + 0.1 x y - 14 x - 10 y + 2000

e x t re m e f (x) = x^{2} - 11 x + 24

e x t re m e \frac{x ^{3} + 1}{x}