What is the extreme f(x)=4+27x-x^3 ?

The extreme f(x)=4+27x-x^3 is Minimum(-3,-50),Maximum(3,58)

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extreme f(x)=4+27x-x^3

extreme points

f (x) = 4 + 27 x - x^{3}

Minimum (- 3, - 50), Maximum (3, 58)

Solution steps

f^{'} (x) = - 3 x^{2} + 27

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

4 + 27 x - x^{3} : - 50

Minimum (- 3, - 50)

Plug

x = 3

into

4 + 27 x - x^{3} : 58

Maximum (3, 58)

Minimum (- 3, - 50), Maximum (3, 58)

What is the extreme f(x)=4+27x-x^3 ?
The extreme f(x)=4+27x-x^3 is Minimum(-3,-50),Maximum(3,58)