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

The extreme f(x)=(x+2)^3(x-3) is Saddle(-2,0),Minimum(7/4 ,-16875/256)

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

extreme points

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

Saddle (- 2, 0), Minimum (\frac{7}{4}, - \frac{16875}{256})

Solution steps

f^{'} (x) = (x + 2)^{2} (4 x - 7)

Find intervals:

Decreasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < \frac{7}{4},

Increasing

: \frac{7}{4} < x < \infty

Plug

x = - 2

into

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

Saddle (- 2, 0)

Plug

x = \frac{7}{4}

into

(x + 2)^{3} (x - 3) : - \frac{16875}{256}

Minimum (\frac{7}{4}, - \frac{16875}{256})

Saddle (- 2, 0), Minimum (\frac{7}{4}, - \frac{16875}{256})

f (x) = (x - 1) (x - 6)^{3} + 6, 1 \leq x \leq 4

f (x) = x^{4} - 5 x^{3} + x^{2} + 21 x - 18

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

g (x, y) = e^{x} - x + e^{y} - y

\frac{1}{3 - 2 x - x ^{2}}

What is the extreme f(x)=(x+2)^3(x-3) ?
The extreme f(x)=(x+2)^3(x-3) is Saddle(-2,0),Minimum(7/4 ,-16875/256)