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

The extreme f(x)=(x-2)(x-3)^2 is Maximum(7/3 , 4/27),Minimum(3,0)

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

extreme points

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

Maximum (\frac{7}{3}, \frac{4}{27}), Minimum (3, 0)

Solution steps

f^{'} (x) = (x - 3) (3 x - 7)

Find intervals:

Increasing

: - \infty < x < \frac{7}{3},

Decreasing

: \frac{7}{3} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = \frac{7}{3}

into

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

Maximum (\frac{7}{3}, \frac{4}{27})

Plug

x = 3

into

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

Minimum (3, 0)

Maximum (\frac{7}{3}, \frac{4}{27}), Minimum (3, 0)

f (x) = \frac{x + 2}{3}

\frac{2 x - 5}{x ^{2} - 4}

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

(2) (5)

f (x) = cot (x)

What is the extreme f(x)=(x-2)(x-3)^2 ?
The extreme f(x)=(x-2)(x-3)^2 is Maximum(7/3 , 4/27),Minimum(3,0)