What is the extreme f(x)=(27x)/(x^2+9) ?

The extreme f(x)=(27x)/(x^2+9) is Minimum(-3,-9/2),Maximum(3, 9/2)

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extreme f(x)=(27x)/(x^2+9)

extreme points

f (x) = \frac{27 x}{x ^{2} + 9}

Minimum (- 3, - \frac{9}{2}), Maximum (3, \frac{9}{2})

Solution steps

f^{'} (x) = \frac{27 ( - x ^{2} + 9 )}{( x ^{2} + 9 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

\frac{27 x}{x ^{2} + 9} : - \frac{9}{2}

Minimum (- 3, - \frac{9}{2})

Plug

x = 3

into

\frac{27 x}{x ^{2} + 9} : \frac{9}{2}

Maximum (3, \frac{9}{2})

Minimum (- 3, - \frac{9}{2}), Maximum (3, \frac{9}{2})

What is the extreme f(x)=(27x)/(x^2+9) ?
The extreme f(x)=(27x)/(x^2+9) is Minimum(-3,-9/2),Maximum(3, 9/2)