What is the extreme y=(x-2)^3(x+2) ?

The extreme y=(x-2)^3(x+2) is Minimum(-1,-27),Saddle(2,0)

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extreme y=(x-2)^3(x+2)

extreme points

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

Minimum (- 1, - 27), Saddle (2, 0)

Solution steps

f^{'} (x) = 4 (x - 2)^{2} (x + 1)

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 1

into

(x - 2)^{3} (x + 2) : - 27

Minimum (- 1, - 27)

Plug

x = 2

into

(x - 2)^{3} (x + 2) : 0

Saddle (2, 0)

Minimum (- 1, - 27), Saddle (2, 0)

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What is the extreme y=(x-2)^3(x+2) ?
The extreme y=(x-2)^3(x+2) is Minimum(-1,-27),Saddle(2,0)