What is the extreme f(x)=(ln(x))/(5x^2) ?

The extreme f(x)=(ln(x))/(5x^2) is Maximum(sqrt(e), 1/(10e))

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extreme f(x)=(ln(x))/(5x^2)

extreme points

f (x) = \frac{ln ( x )}{5 x ^{2}}

Maximum (e, \frac{1}{10 e})

Solution steps

f^{'} (x) = \frac{1 - 2 ln ( x )}{5 x ^{3}}

Find intervals:

Increasing

: 0 < x < e,

Decreasing

: e < x < \infty

Plug

x = e

into

\frac{ln ( x )}{5 x ^{2}} : \frac{1}{10 e}

Maximum (e, \frac{1}{10 e})

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

2800 x - x^{3} + 3 x^{2} + 80 x - 500

f (x) = y = \frac{1}{3} x^{3} - 6 x + 1, - 1 \leq x \leq 6

y = 5 - (x + 1)^{2}

f (x, y) = - x^{2} + 5 y^{2} + 10 x - 10 y - 28

What is the extreme f(x)=(ln(x))/(5x^2) ?
The extreme f(x)=(ln(x))/(5x^2) is Maximum(sqrt(e), 1/(10e))