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

The extreme f(x)=(x+2)^2(x-3) is Maximum(-2,0),Minimum(4/3 ,-500/27)

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

extreme

Maximum (- 2, 0), Minimum (\frac{4}{3}, - \frac{500}{27})

Solution steps

f^{'} (x) = (x + 2) (3 x - 4)

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < \frac{4}{3},

Increasing

: \frac{4}{3} < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, 0)

Plug

x = \frac{4}{3}

into

(x + 2)^{2} (x - 3) : - \frac{500}{27}

Minimum (\frac{4}{3}, - \frac{500}{27})

Maximum (- 2, 0), Minimum (\frac{4}{3}, - \frac{500}{27})

What is the extreme f(x)=(x+2)^2(x-3) ?
The extreme f(x)=(x+2)^2(x-3) is Maximum(-2,0),Minimum(4/3 ,-500/27)