What is the extreme f(x)=xln(x^2) ?

The extreme f(x)=xln(x^2) is Maximum(-1/e , 2/e),Minimum(1/e ,-2/e)

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extreme f(x)=xln(x^2)

extreme points

f (x) = x ln (x^{2})

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{1}{e},

Decreasing

: - \frac{1}{e} < x < 0,

Decreasing

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

Increasing

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

Plug

x = - \frac{1}{e}

into

x ln (x^{2}) : \frac{2}{e}

Maximum (- \frac{1}{e}, \frac{2}{e})

Plug

x = \frac{1}{e}

into

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

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

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

f (x) = \frac{x ^{2} - 11 x + 67}{x - 9}

f (x) = - x^{3} + 3 x + 7

f (x) = x ln (9 x)

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

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

What is the extreme f(x)=xln(x^2) ?
The extreme f(x)=xln(x^2) is Maximum(-1/e , 2/e),Minimum(1/e ,-2/e)