What is the extreme f(x)= x/(x^2+25) ?

The extreme f(x)= x/(x^2+25) is Minimum(-5,-1/10),Maximum(5, 1/10)

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extreme f(x)= x/(x^2+25)

extreme points

f (x) = \frac{x}{x ^{2} + 25}

Minimum (- 5, - \frac{1}{10}), Maximum (5, \frac{1}{10})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 25}{( x ^{2} + 25 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 5

into

\frac{x}{x ^{2} + 25} : - \frac{1}{10}

Minimum (- 5, - \frac{1}{10})

Plug

x = 5

into

\frac{x}{x ^{2} + 25} : \frac{1}{10}

Maximum (5, \frac{1}{10})

Minimum (- 5, - \frac{1}{10}), Maximum (5, \frac{1}{10})

f (x, y) = 4 - \frac{1}{9} x^{2} - \frac{1}{16} y^{2}

f (x) = ln (\frac{1}{x + y})

f (x) = x^{2} e^{x} [- 3.1]

\frac{1}{x ^{2} - 1}

f (x) = x^{3} - 5 x^{2} + 3 x + 12

What is the extreme f(x)= x/(x^2+25) ?
The extreme f(x)= x/(x^2+25) is Minimum(-5,-1/10),Maximum(5, 1/10)