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

The extreme f(x)=(x-2)^2(x+3)^3 is Saddle(-3,0),Maximum(0,108),Minimum(2,0)

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

extreme

Saddle (- 3, 0), Maximum (0, 108), Minimum (2, 0)

Solution steps

f^{'} (x) = 5 x (x + 3)^{2} (x - 2)

Find intervals:

Increasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 3

into

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

Saddle (- 3, 0)

Plug

x = 0

into

(x - 2)^{2} (x + 3)^{3} : 108

Maximum (0, 108)

Plug

x = 2

into

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

Minimum (2, 0)

Saddle (- 3, 0), Maximum (0, 108), Minimum (2, 0)

What is the extreme f(x)=(x-2)^2(x+3)^3 ?
The extreme f(x)=(x-2)^2(x+3)^3 is Saddle(-3,0),Maximum(0,108),Minimum(2,0)