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

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

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

extreme points

f (x) = x 2 - x

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

Solution steps

f^{'} (x) = \frac{- 3 x + 4}{2 2 - x}

Find intervals:

Increasing

: - \infty < x < \frac{4}{3},

Decreasing

: \frac{4}{3} < x < 2

Plug

x = \frac{4}{3}

into

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

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

Plug

x = 2

into

x 2 - x : 0

Minimum (2, 0)

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

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

f (x, y, z) = x + y 2 + x 3

f (x) = \frac{x ^{2} + x - 38}{x ^{2} - 25}

f (x) = x^{\frac{4}{3}} + 4 x^{\frac{1}{3}}

h (x) = - 3 x^{5} + 5 x^{3}

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