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

The extreme f(x)=(x+2)^3(x-3)^2 is Saddle(-2,0),Maximum(1,108),Minimum(3,0)

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

extreme points

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

Saddle (- 2, 0), Maximum (1, 108), Minimum (3, 0)

Solution steps

f^{'} (x) = 5 (x + 2)^{2} (x - 3) (x - 1)

Find intervals:

Increasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 2

into

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

Saddle (- 2, 0)

Plug

x = 1

into

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

Maximum (1, 108)

Plug

x = 3

into

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

Minimum (3, 0)

Saddle (- 2, 0), Maximum (1, 108), Minimum (3, 0)

y = (x - 1)^{2} (x + 1)

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

f (x) = 5 x^{2} - 20 x + 5, 0 \leq x \leq 3

f (x) = x^{\frac{2}{3}} (\frac{1}{8} x^{2} + \frac{3}{5} x - 9)

f (x) = 5 - 8 x, x \geq 1

What is the extreme f(x)=(x+2)^3(x-3)^2 ?
The extreme f(x)=(x+2)^3(x-3)^2 is Saddle(-2,0),Maximum(1,108),Minimum(3,0)