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

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

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extreme (x-2)^3*(x+2)

extreme points

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

Minimum (- 1, - 27)

Plug

x = 2

into

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

Saddle (2, 0)

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

f (x) = \frac{x + 2}{x ^{2} - 7 x - 18}

5 x y - 7 x^{2} + 3 x - 6 y + 2

f (x) = 3 x^{2} - 6 x + 2

y = x^{2} - 6 x + 10

f (x) = 4 x^{3} - 48 x - 1

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