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

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})

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)