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

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

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

extreme

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 3

into

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

Maximum (- 3, 32)

Plug

x = 1

into

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

Minimum (1, 0)

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

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