extreme (e^{-x})/((1+e^{-x))^2}

解答

极值点

\frac{e ^{- x}}{( 1 + e ^{- x} ) ^{2}}

极大值 (0, \frac{1}{4})

求解步骤

f^{'} (x) = \frac{e ^{- 2 x} ( - e ^{x} + 1 )}{( 1 + e ^{- x} ) ^{3}}

Find intervals:

递增

: - \infty < x < 0,

递减

: 0 < x < \infty

将

x = 0

代入

\frac{e ^{- x}}{( 1 + e ^{- x} ) ^{2}} : \frac{1}{4}

极大值 (0, \frac{1}{4})

e x t re m e f (x) = x^{3} - 4 x^{2} + 4 x - 1

e x t re m e f (x) = 3 (x^{2} + 4) (x^{2} + 8)^{2}

e x t re m e f (x) = \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 2 x + 1

e x t re m e f (x, y) = \frac{1}{3} x^{2} + 2 x y + 3 y^{2} + 4 x - 1

e x t re m e f (x, y) = 4 x + 6 y - x^{2} - y^{2} + 8