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

The extreme f(x)=(x-3)(x-2)^2 is Maximum(2,0),Minimum(8/3 ,-4/27)

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

extreme

Maximum (2, 0), Minimum (\frac{8}{3}, - \frac{4}{27})

Solution steps

f^{'} (x) = (x - 2) (3 x - 8)

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < \frac{8}{3},

Increasing

: \frac{8}{3} < x < \infty

Plug

x = 2

into

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

Maximum (2, 0)

Plug

x = \frac{8}{3}

into

(x - 3) (x - 2)^{2} : - \frac{4}{27}

Minimum (\frac{8}{3}, - \frac{4}{27})

Maximum (2, 0), Minimum (\frac{8}{3}, - \frac{4}{27})

What is the extreme f(x)=(x-3)(x-2)^2 ?
The extreme f(x)=(x-3)(x-2)^2 is Maximum(2,0),Minimum(8/3 ,-4/27)