What is the extreme f(x)= x/(49+x^2) ?

The extreme f(x)= x/(49+x^2) is Minimum(-7,-1/14),Maximum(7, 1/14)

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extreme f(x)= x/(49+x^2)

extreme

Minimum (- 7, - \frac{1}{14}), Maximum (7, \frac{1}{14})

Solution steps

f^{'} (x) = \frac{49 - x ^{2}}{( 49 + x ^{2} ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 7,

Increasing

: - 7 < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = - 7

into

\frac{x}{49 + x ^{2}} : - \frac{1}{14}

Minimum (- 7, - \frac{1}{14})

Plug

x = 7

into

\frac{x}{49 + x ^{2}} : \frac{1}{14}

Maximum (7, \frac{1}{14})

Minimum (- 7, - \frac{1}{14}), Maximum (7, \frac{1}{14})

What is the extreme f(x)= x/(49+x^2) ?
The extreme f(x)= x/(49+x^2) is Minimum(-7,-1/14),Maximum(7, 1/14)