What is the extreme f(x)=sqrt(x)*ln(x) ?

The extreme f(x)=sqrt(x)*ln(x) is Minimum(1/(e^2),-2/e)

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extreme f(x)=sqrt(x)*ln(x)

extreme points

f (x) = x \cdot ln (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 \cdot ln (x) : - \frac{2}{e}

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

f (x, y) = 2 x^{2} + 3 x y + y^{2} + 0 x + 5

f (x, y) = y^{2} (x - 1)^{2} + x^{2} (y + 4)^{2}

f (x) = (x - 2)^{2} + 1

2 x^{3} - 3 x^{2} - 12 x + 1

f (x) = 324 x - 72 x^{2} + 4 x^{3}

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