What is the extreme f(x)=sqrt(x)ln(10x) ?

The extreme f(x)=sqrt(x)ln(10x) is Minimum(1/(10e^2),-(sqrt(2))/(sqrt(5)e))

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extreme f(x)=sqrt(x)ln(10x)

extreme points

f (x) = x ln (10 x)

Minimum (\frac{1}{10 e ^{2}}, - \frac{2}{5 e})

Solution steps

f^{'} (x) = \frac{ln ( 10 x )}{2 x} + \frac{1}{x}

Find intervals:

Decreasing

: 0 < x < \frac{1}{10 e ^{2}},

Increasing

: \frac{1}{10 e ^{2}} < x < \infty

Plug

x = \frac{1}{10 e ^{2}}

into

x ln (10 x) : - \frac{2}{5 e}

Minimum (\frac{1}{10 e ^{2}}, - \frac{2}{5 e})

f (x) = 8 y^{2} + x^{2} - x^{2} y

f (x) = \frac{4 x - 3}{x}

f (x) = \frac{x ^{2} - 1}{- 5 x + \frac{1}{2}}

f (x) = - 2 x^{3} - 33 x^{2} - 108 x - 1

3 x + 1

What is the extreme f(x)=sqrt(x)ln(10x) ?
The extreme f(x)=sqrt(x)ln(10x) is Minimum(1/(10e^2),-(sqrt(2))/(sqrt(5)e))