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 points

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

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})

y = 7 x + 7 sin (x)

f (x) = 4 x^{2} + 3 x^{2} - 6 x + 1

\frac{4 x + 13}{- 2 x - 6}

y = x^{4} - 12 x^{3} + 48 x^{2} - 64 x

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

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)