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

The extreme f(x)=(x-1)^2*(x-3)+2 is Maximum(1,2),Minimum(7/3 , 22/27)

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

extreme

Maximum (1, 2), Minimum (\frac{7}{3}, \frac{22}{27})

Solution steps

f^{'} (x) = 3 x^{2} - 10 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} \cdot (x - 3) + 2 : 2

Maximum (1, 2)

Plug

x = \frac{7}{3}

into

(x - 1)^{2} \cdot (x - 3) + 2 : \frac{22}{27}

Minimum (\frac{7}{3}, \frac{22}{27})

Maximum (1, 2), Minimum (\frac{7}{3}, \frac{22}{27})

What is the extreme f(x)=(x-1)^2*(x-3)+2 ?
The extreme f(x)=(x-1)^2*(x-3)+2 is Maximum(1,2),Minimum(7/3 , 22/27)