extreme f(x)=(x-8)ln(x-8)

解答

极值点

f (x) = (x - 8) ln (x - 8)

极小值 (\frac{1}{e} + 8, - \frac{1}{e})

求解步骤

f^{'} (x) = ln (x - 8) + 1

Find intervals:

递减

: 8 < x < \frac{1}{e} + 8,

递增

: \frac{1}{e} + 8 < x < \infty

将

x = \frac{1}{e} + 8

代入

(x - 8) ln (x - 8) : - \frac{1}{e}

极小值 (\frac{1}{e} + 8, - \frac{1}{e})

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

e x t re m e f (x) = x^{4} - 98 x^{2} + 4

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

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

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