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Popular Functions >

extreme (ln(x^2))/x

Solution

extreme

Solution

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - e,

Increasing

: - e < x < 0,

Increasing

: 0 < x < e,

Decreasing

: e < x < \infty

Plug

x = - e

into

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

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

Plug

x = e

into

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

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

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

Graph

Popular Examples

extreme t-\sqrt[3]{t}

extreme f(x)=7xsqrt(x-x^2)

extreme f(x)=3x^4-12x^3

extreme f(x)=x^3-x^2-12+2,0<= x<= 4

extreme f(x)=(x^2)/(x^2+108)

Frequently Asked Questions (FAQ)

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