What is the extreme f(x)=(x-5)ln(x-5) ?

The extreme f(x)=(x-5)ln(x-5) is Minimum(1/e+5,-1/e)

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

extreme points

f (x) = (x - 5) ln (x - 5)

Minimum (\frac{1}{e} + 5, - \frac{1}{e})

Solution steps

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

Find intervals:

Decreasing

: 5 < x < \frac{1}{e} + 5,

Increasing

: \frac{1}{e} + 5 < x < \infty

Plug

x = \frac{1}{e} + 5

into

(x - 5) ln (x - 5) : - \frac{1}{e}

Minimum (\frac{1}{e} + 5, - \frac{1}{e})

f (x) = x^{2} + 5 x + 6

f (x) = 2 sec (x) - tan (x)

f (x) = \frac{x ^{2} - 9 x + 39}{x - 7}

4 x^{2} - 8 x + 16

x + \frac{3}{x}

What is the extreme f(x)=(x-5)ln(x-5) ?
The extreme f(x)=(x-5)ln(x-5) is Minimum(1/e+5,-1/e)