What is the extreme f(x)=sqrt(x)log_{e}(x) ?

The extreme f(x)=sqrt(x)log_{e}(x) is Minimum(1/(e^2),-2/e)

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extreme f(x)=sqrt(x)log_{e}(x)

extreme points

f (x) = x lo g_{e} (x)

Minimum (\frac{1}{e ^{2}}, - \frac{2}{e})

Solution steps

f^{'} (x) = \frac{ln ( x )}{2 x} + \frac{1}{x}

Find intervals:

Decreasing

: 0 < x < \frac{1}{e ^{2}},

Increasing

: \frac{1}{e ^{2}} < x < \infty

Plug

x = \frac{1}{e ^{2}}

into

x lo g_{e} (x) : - \frac{2}{e}

Minimum (\frac{1}{e ^{2}}, - \frac{2}{e})

What is the extreme f(x)=sqrt(x)log_{e}(x) ?
The extreme f(x)=sqrt(x)log_{e}(x) is Minimum(1/(e^2),-2/e)