What is the extreme f(x)=9x-x^3 ?

The extreme f(x)=9x-x^3 is Minimum(-sqrt(3),-6sqrt(3)),Maximum(sqrt(3),6sqrt(3))

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extreme f(x)=9x-x^3

extreme points

f (x) = 9 x - x^{3}

Minimum (- 3, - 63), Maximum (3, 63)

Solution steps

f^{'} (x) = 9 - 3 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

9 x - x^{3} : - 63

Minimum (- 3, - 63)

Plug

x = 3

into

9 x - x^{3} : 63

Maximum (3, 63)

Minimum (- 3, - 63), Maximum (3, 63)

What is the extreme f(x)=9x-x^3 ?
The extreme f(x)=9x-x^3 is Minimum(-sqrt(3),-6sqrt(3)),Maximum(sqrt(3),6sqrt(3))