What is the extreme f(x)=sqrt(x)ln(6x) ?

The extreme f(x)=sqrt(x)ln(6x) is Minimum(1/(6e^2),-(sqrt(2))/(sqrt(3)e))

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extreme f(x)=sqrt(x)ln(6x)

extreme points

f (x) = x ln (6 x)

Minimum (\frac{1}{6 e ^{2}}, - \frac{2}{3 e})

Solution steps

f^{'} (x) = \frac{ln ( 6 x )}{2 x} + \frac{1}{x}

Find intervals:

Decreasing

: 0 < x < \frac{1}{6 e ^{2}},

Increasing

: \frac{1}{6 e ^{2}} < x < \infty

Plug

x = \frac{1}{6 e ^{2}}

into

x ln (6 x) : - \frac{2}{3 e}

Minimum (\frac{1}{6 e ^{2}}, - \frac{2}{3 e})

f (x) = - x^{3} + 3 x^{2} + 24 x + 2

432 y^{783}

f (x) = 2 x^{3} - 3 x^{3} - 12 x + 1

f (x) = 4 x^{4} - 2 a^{2} x^{3}

f (x) = x^{4} + 4 x^{3} - 20 x^{2} + 1

What is the extreme f(x)=sqrt(x)ln(6x) ?
The extreme f(x)=sqrt(x)ln(6x) is Minimum(1/(6e^2),-(sqrt(2))/(sqrt(3)e))