extreme f(x)=(5-x)5^x

解答

极值点

f (x) = (5 - x) 5^{x}

极大值 (- \frac{1}{ln ( 5 )} + 5, \frac{5 ^{\frac{- 1 + 5 l n ( 5 )}{l n ( 5 )}}}{ln ( 5 )})

求解步骤

f^{'} (x) = 5^{x} (- 1 - ln (5) (x - 5))

Find intervals:

递增

: - \infty < x < - \frac{1}{ln ( 5 )} + 5,

递减

: - \frac{1}{ln ( 5 )} + 5 < x < \infty

将

x = - \frac{1}{ln ( 5 )} + 5

代入

(5 - x) 5^{x} : \frac{5 ^{\frac{- 1 + 5 l n ( 5 )}{l n ( 5 )}}}{ln ( 5 )}

极大值 (- \frac{1}{ln ( 5 )} + 5, \frac{5 ^{\frac{- 1 + 5 l n ( 5 )}{l n ( 5 )}}}{ln ( 5 )})

e x t re m e f (x) = - 4 4 x^{2} + y^{2} + 81

e x t re m e 2 x^{3} - 33 x^{2} + 108 x + 5

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

e x t re m e x^{3} - 6 x^{2} + 2 x - 2

e x t re m e f (x) = x + \frac{4}{x}, 1 \leq x \leq 10