What is the extreme f(x)=(x-1)^2(x+3)^2 ?

The extreme f(x)=(x-1)^2(x+3)^2 is Minimum(-3,0),Maximum(-1,16),Minimum(1,0)

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extreme f(x)=(x-1)^2(x+3)^2

extreme points

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

Minimum (- 3, 0), Maximum (- 1, 16), Minimum (1, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < - 1,

Decreasing

: - 1 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 3

into

(x - 1)^{2} (x + 3)^{2} : 0

Minimum (- 3, 0)

Plug

x = - 1

into

(x - 1)^{2} (x + 3)^{2} : 16

Maximum (- 1, 16)

Plug

x = 1

into

(x - 1)^{2} (x + 3)^{2} : 0

Minimum (1, 0)

Minimum (- 3, 0), Maximum (- 1, 16), Minimum (1, 0)

y = x^{2} - 7 x - 4

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

f (x) = 3 sin (x) + 7 cos (x), 0 \leq x \leq 2 π

U (a, b) = aa + bb

f (x) = \frac{1}{3} x^{3} - 7 x^{2} + 24 x + 6

What is the extreme f(x)=(x-1)^2(x+3)^2 ?
The extreme f(x)=(x-1)^2(x+3)^2 is Minimum(-3,0),Maximum(-1,16),Minimum(1,0)