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

The extreme 3(x-2)^2(x-1)+(x-2)^2 is Maximum(10/9 , 256/243),Minimum(2,0)

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extreme 3(x-2)^2(x-1)+(x-2)^2

extreme

Maximum (\frac{10}{9}, \frac{256}{243}), Minimum (2, 0)

Solution steps

f^{'} (x) = 9 x^{2} - 28 x + 20

Find intervals:

Increasing

: - \infty < x < \frac{10}{9},

Decreasing

: \frac{10}{9} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = \frac{10}{9}

into

3 (x - 2)^{2} (x - 1) + (x - 2)^{2} : \frac{256}{243}

Maximum (\frac{10}{9}, \frac{256}{243})

Plug

x = 2

into

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

Minimum (2, 0)

Maximum (\frac{10}{9}, \frac{256}{243}), Minimum (2, 0)

What is the extreme 3(x-2)^2(x-1)+(x-2)^2 ?
The extreme 3(x-2)^2(x-1)+(x-2)^2 is Maximum(10/9 , 256/243),Minimum(2,0)