What is the extreme (ln(x^2))/(x^2) ?

The extreme (ln(x^2))/(x^2) is Maximum(-sqrt(e), 1/e),Maximum(sqrt(e), 1/e)

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extreme (ln(x^2))/(x^2)

extreme points

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

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

Solution steps

f^{'} (x) = \frac{2 ( - ln ( x ^{2} ) + 1 )}{x ^{3}}

Find intervals:

Increasing

: - \infty < x < - e,

Decreasing

: - e < x < 0,

Increasing

: 0 < x < e,

Decreasing

: e < x < \infty

Plug

x = - e

into

\frac{ln ( x ^{2} )}{x ^{2}} : \frac{1}{e}

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

Plug

x = e

into

\frac{ln ( x ^{2} )}{x ^{2}} : \frac{1}{e}

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

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

f (x) = x^{3} - 12 x^{2} + 80

f (x) = 20 y - 2 x^{2} - 4 x y - y^{2} + 30 x

f (x, y) = x^{2} + 4 x y + y^{2}

f (x, y) = x^{2} y + 12 x^{2} + \frac{3 y ^{2}}{2} + 5

f (x) = x^{\frac{2}{3}}, - 1 \leq x \leq 27

What is the extreme (ln(x^2))/(x^2) ?
The extreme (ln(x^2))/(x^2) is Maximum(-sqrt(e), 1/e),Maximum(sqrt(e), 1/e)