What is the extreme-(x+1)(x-1)^2 ?

The extreme-(x+1)(x-1)^2 is Minimum(-1/3 ,-32/27),Maximum(1,0)

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Find the Local Maxima and Minima -(x+1)(x-1)^2

extreme points

- (x + 1) (x - 1)^{2}

Minimum (- \frac{1}{3}, - \frac{32}{27}), Maximum (1, 0)

Solution steps

f^{'} (x) = - 3 x^{2} + 2 x + 1

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{3},

Increasing

: - \frac{1}{3} < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

- (x + 1) (x - 1)^{2} : - \frac{32}{27}

Minimum (- \frac{1}{3}, - \frac{32}{27})

Plug

x = 1

into

- (x + 1) (x - 1)^{2} : 0

Maximum (1, 0)

Minimum (- \frac{1}{3}, - \frac{32}{27}), Maximum (1, 0)

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

x

f (x) = \frac{x}{( x ^{2} + 1 )}

f (c) = - 44 c

f (x) = 8 - x, (- 3, 5)

What is the extreme-(x+1)(x-1)^2 ?
The extreme-(x+1)(x-1)^2 is Minimum(-1/3 ,-32/27),Maximum(1,0)