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

The extreme f(x)=(x+2)^3(x-3)^3 is Saddle(-2,0),Minimum(1/2 ,-15625/64),Saddle(3,0)

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

extreme points

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

Saddle (- 2, 0), Minimum (\frac{1}{2}, - \frac{15625}{64}), Saddle (3, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 2

into

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

Saddle (- 2, 0)

Plug

x = \frac{1}{2}

into

(x + 2)^{3} (x - 3)^{3} : - \frac{15625}{64}

Minimum (\frac{1}{2}, - \frac{15625}{64})

Plug

x = 3

into

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

Saddle (3, 0)

Saddle (- 2, 0), Minimum (\frac{1}{2}, - \frac{15625}{64}), Saddle (3, 0)

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

f (x, y) = 6 x^{2} - x y + 4 y^{2}

f (x) = \frac{x + 5}{x ^{2} - 2 x - 35}

What is the extreme f(x)=(x+2)^3(x-3)^3 ?
The extreme f(x)=(x+2)^3(x-3)^3 is Saddle(-2,0),Minimum(1/2 ,-15625/64),Saddle(3,0)