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

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

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

extreme

Minimum (0, 0), Maximum (\frac{3}{2}, \frac{3 3}{4}), Minimum (2, 0)

Solution steps

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

Find intervals:

Increasing

: 0 < x < \frac{3}{2},

Decreasing

: \frac{3}{2} < x < 2

Plug

x = 0

into

x 2 x - x^{2} : 0

Minimum (0, 0)

Plug

x = \frac{3}{2}

into

x 2 x - x^{2} : \frac{3 3}{4}

Maximum (\frac{3}{2}, \frac{3 3}{4})

Plug

x = 2

into

x 2 x - x^{2} : 0

Minimum (2, 0)

Minimum (0, 0), Maximum (\frac{3}{2}, \frac{3 3}{4}), Minimum (2, 0)

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