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

The extreme f(x)=(x-1)^2(x-3) is Maximum(1,0),Minimum(7/3 ,-32/27)

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extreme f(x)=(x-1)^2(x-3)

extreme

Maximum (1, 0), Minimum (\frac{7}{3}, - \frac{32}{27})

Solution steps

f^{'} (x) = (x - 1) (3 x - 7)

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

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

Increasing

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

Plug

x = 1

into

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

Maximum (1, 0)

Plug

x = \frac{7}{3}

into

(x - 1)^{2} (x - 3) : - \frac{32}{27}

Minimum (\frac{7}{3}, - \frac{32}{27})

Maximum (1, 0), Minimum (\frac{7}{3}, - \frac{32}{27})

What is the extreme f(x)=(x-1)^2(x-3) ?
The extreme f(x)=(x-1)^2(x-3) is Maximum(1,0),Minimum(7/3 ,-32/27)