What is the extreme g(x)=(x-2)^3(x+1)^2 ?

The extreme g(x)=(x-2)^3(x+1)^2 is Maximum(-1,0),Minimum(1/5 ,-26244/3125),Saddle(2,0)

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extreme g(x)=(x-2)^3(x+1)^2

extreme points

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

Maximum (- 1, 0), Minimum (\frac{1}{5}, - \frac{26244}{3125}), Saddle (2, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < \frac{1}{5},

Increasing

: \frac{1}{5} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 1

into

(x - 2)^{3} (x + 1)^{2} : 0

Maximum (- 1, 0)

Plug

x = \frac{1}{5}

into

(x - 2)^{3} (x + 1)^{2} : - \frac{26244}{3125}

Minimum (\frac{1}{5}, - \frac{26244}{3125})

Plug

x = 2

into

(x - 2)^{3} (x + 1)^{2} : 0

Saddle (2, 0)

Maximum (- 1, 0), Minimum (\frac{1}{5}, - \frac{26244}{3125}), Saddle (2, 0)

What is the extreme g(x)=(x-2)^3(x+1)^2 ?
The extreme g(x)=(x-2)^3(x+1)^2 is Maximum(-1,0),Minimum(1/5 ,-26244/3125),Saddle(2,0)