What is the extreme f(x)=(5-x)(x+1)^2 ?

The extreme f(x)=(5-x)(x+1)^2 is Minimum(-1,0),Maximum(3,32)

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extreme f(x)=(5-x)(x+1)^2

extreme points

f (x) = (5 - x) (x + 1)^{2}

Minimum (- 1, 0), Maximum (3, 32)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, 0)

Plug

x = 3

into

(5 - x) (x + 1)^{2} : 32

Maximum (3, 32)

Minimum (- 1, 0), Maximum (3, 32)

f (x, y) = 4 x^{2} - 12 x + y^{2} + 2 y - 10

x^{4} - 8 x^{2} + 1

f (x, y) = \frac{9}{3} x^{2} y + y^{3} - 2 x y^{2}

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

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

What is the extreme f(x)=(5-x)(x+1)^2 ?
The extreme f(x)=(5-x)(x+1)^2 is Minimum(-1,0),Maximum(3,32)