What is the extreme f(x)=(x-4)ln(x-4) ?

The extreme f(x)=(x-4)ln(x-4) is Minimum(1/e+4,-1/e)

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extreme f(x)=(x-4)ln(x-4)

extreme points

f (x) = (x - 4) ln (x - 4)

Minimum (\frac{1}{e} + 4, - \frac{1}{e})

Solution steps

f^{'} (x) = ln (x - 4) + 1

Find intervals:

Decreasing

: 4 < x < \frac{1}{e} + 4,

Increasing

: \frac{1}{e} + 4 < x < \infty

Plug

x = \frac{1}{e} + 4

into

(x - 4) ln (x - 4) : - \frac{1}{e}

Minimum (\frac{1}{e} + 4, - \frac{1}{e})

f (x, y) = x y^{2} + x^{3} y - x y

f (x, y) = 5 x^{2} + x y^{2} + y^{2}

f (x) = 1 + 12 x - x^{3}

f (x) = x^{3} + 3 x^{2} - 9 x - 3

f (x) = - x^{3} - 8 x

What is the extreme f(x)=(x-4)ln(x-4) ?
The extreme f(x)=(x-4)ln(x-4) is Minimum(1/e+4,-1/e)