extreme e^{6x}+e^{-x}

解答

极值点

e^{6 x} + e^{- x}

极小值 (- \frac{ln ( 6 )}{7}, \frac{1}{e ^{\frac{6 l n ( 6 )}{7}}} + e^{\frac{l n ( 6 )}{7}})

求解步骤

f^{'} (x) = e^{6 x} \cdot 6 - e^{- x}

Find intervals:

递减

: - \infty < x < - \frac{1}{7} ln (6),

递增

: - \frac{1}{7} ln (6) < x < \infty

将

x = - \frac{ln ( 6 )}{7}

代入

e^{6 x} + e^{- x} : \frac{1}{e ^{\frac{6 l n ( 6 )}{7}}} + e^{\frac{l n ( 6 )}{7}}

极小值 (- \frac{ln ( 6 )}{7}, \frac{1}{e ^{\frac{6 l n ( 6 )}{7}}} + e^{\frac{l n ( 6 )}{7}})

e x t re m e F (x, y) = 12 x^{2} + 5 x y - 17 x + 7 y - 2 y^{2} + 5

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

e x t re m e f (x, y) = 3 x^{3} - 2 x^{2} y + 5 x y - y^{3} - 1

e x t re m e f (x) = (3 - x) e^{x - 3}

e x t re m e f (x) = 1 + x^{2} e^{5 - 3 x}