What is the extreme f(x)=3x^3-81x ?

The extreme f(x)=3x^3-81x is Maximum(-3,162),Minimum(3,-162)

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extreme f(x)=3x^3-81x

extreme points

f (x) = 3 x^{3} - 81 x

Maximum (- 3, 162), Minimum (3, - 162)

Solution steps

f^{'} (x) = 9 x^{2} - 81

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

3 x^{3} - 81 x : 162

Maximum (- 3, 162)

Plug

x = 3

into

3 x^{3} - 81 x : - 162

Minimum (3, - 162)

Maximum (- 3, 162), Minimum (3, - 162)

What is the extreme f(x)=3x^3-81x ?
The extreme f(x)=3x^3-81x is Maximum(-3,162),Minimum(3,-162)