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

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

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extreme f(x)=2xln|x|

extreme points

f (x) = 2 x ln ∣ x ∣

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

Solution steps

Find the critical points:

x = - \frac{1}{e}, x = \frac{1}{e}

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 the extreme point

x = - \frac{1}{e}

into

2 x ln ∣ x ∣ \Rightarrow y = \frac{2}{e}

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

Plug the extreme point

x = \frac{1}{e}

into

2 x ln ∣ x ∣ \Rightarrow y = - \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, y) = x^{2} + y^{2} - 2 x

f (x) = x^{3} + 8

f (x) = \frac{900}{x} + 2 π x^{2}

\frac{ln ( x )}{x ^{3}}

f (x) = - (25 - x^{2})^{2}

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