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

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

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

extreme

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 5

into

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

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

Plug

x = 5

into

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

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

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

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