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

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

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

extreme

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, 0)

Plug

x = 0

into

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

Minimum (0, - 108)

Plug

x = 3

into

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

Saddle (3, 0)

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

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