What is the extreme f(x)=sqrt(x)ln(9x) ?

The extreme f(x)=sqrt(x)ln(9x) is Minimum(1/(9e^2),-2/(3e))

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extreme f(x)=sqrt(x)ln(9x)

extreme points

f (x) = x ln (9 x)

Minimum (\frac{1}{9 e ^{2}}, - \frac{2}{3 e})

Solution steps

f^{'} (x) = \frac{ln ( 9 x )}{2 x} + \frac{1}{x}

Find intervals:

Decreasing

: 0 < x < \frac{1}{9 e ^{2}},

Increasing

: \frac{1}{9 e ^{2}} < x < \infty

Plug

x = \frac{1}{9 e ^{2}}

into

x ln (9 x) : - \frac{2}{3 e}

Minimum (\frac{1}{9 e ^{2}}, - \frac{2}{3 e})

\frac{3 - 14 x - 5 x ^{2}}{3 + 7 x + 2 x ^{2}}

f (x) = x^{\frac{2}{3}} (7 x + 5)

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

f (x) = x - 3 ln (x), \frac{1}{3} \leq x \leq 5

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

What is the extreme f(x)=sqrt(x)ln(9x) ?
The extreme f(x)=sqrt(x)ln(9x) is Minimum(1/(9e^2),-2/(3e))