What is the extreme f(x)= x/(x^2+100) ?

The extreme f(x)= x/(x^2+100) is Minimum(-10,-1/20),Maximum(10, 1/20)

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extreme f(x)= x/(x^2+100)

extreme

Minimum (- 10, - \frac{1}{20}), Maximum (10, \frac{1}{20})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 100}{( x ^{2} + 100 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 10,

Increasing

: - 10 < x < 10,

Decreasing

: 10 < x < \infty

Plug

x = - 10

into

\frac{x}{x ^{2} + 100} : - \frac{1}{20}

Minimum (- 10, - \frac{1}{20})

Plug

x = 10

into

\frac{x}{x ^{2} + 100} : \frac{1}{20}

Maximum (10, \frac{1}{20})

Minimum (- 10, - \frac{1}{20}), Maximum (10, \frac{1}{20})

What is the extreme f(x)= x/(x^2+100) ?
The extreme f(x)= x/(x^2+100) is Minimum(-10,-1/20),Maximum(10, 1/20)