What is the extreme f(x)=9+54x-2x^3 ?

The extreme f(x)=9+54x-2x^3 is Minimum(-3,-99),Maximum(3,117)

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extreme f(x)=9+54x-2x^3

extreme points

f (x) = 9 + 54 x - 2 x^{3}

Minimum (- 3, - 99), Maximum (3, 117)

Solution steps

f^{'} (x) = - 6 x^{2} + 54

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

9 + 54 x - 2 x^{3} : - 99

Minimum (- 3, - 99)

Plug

x = 3

into

9 + 54 x - 2 x^{3} : 117

Maximum (3, 117)

Minimum (- 3, - 99), Maximum (3, 117)

f (x) = 5^{x}

f (x) = x^{2} - 1

f (x) = \frac{x}{2} - 4

f (x) = - x^{2} + 3 x

- 3 x - (x^{2} + 2 x)

What is the extreme f(x)=9+54x-2x^3 ?
The extreme f(x)=9+54x-2x^3 is Minimum(-3,-99),Maximum(3,117)