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Popular >

extreme x/(ln(x^2))

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - e,

Decreasing

: - e < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Decreasing

: 1 < x < e,

Increasing

: e < x < \infty

Plug

x = - e

into

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

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

Plug

x = e

into

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

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

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

Popular Examples

extreme x^{2x}extreme points

x^{2 x}

extreme f(x)=4xy^2+2xy-3y extreme points

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

extreme f(x,y)=(500)/((4+x^2+y^2))extreme points

f (x, y) = \frac{500}{( 4 + x ^{2} + y ^{2} )}

extreme f(x)=(5+x)/(4-x)extreme points

f (x) = \frac{5 + x}{4 - x}

extreme f(x)=7x^2+x-3 extreme points

f (x) = 7 x^{2} + x - 3

Frequently Asked Questions (FAQ)

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