What is the extreme f(x)=xsqrt(1-x) ?

The extreme f(x)=xsqrt(1-x) is Maximum(2/3 , 2/(3sqrt(3))),Minimum(1,0)

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extreme f(x)=xsqrt(1-x)

extreme points

f (x) = x 1 - x

Maximum (\frac{2}{3}, \frac{2}{3 3}), Minimum (1, 0)

Solution steps

f^{'} (x) = \frac{- 3 x + 2}{2 1 - x}

Find intervals:

Increasing

: - \infty < x < \frac{2}{3},

Decreasing

: \frac{2}{3} < x < 1

Plug

x = \frac{2}{3}

into

x 1 - x : \frac{2}{3 3}

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

Plug

x = 1

into

x 1 - x : 0

Minimum (1, 0)

Maximum (\frac{2}{3}, \frac{2}{3 3}), Minimum (1, 0)

f (x) = \frac{x + 1}{2 x + x + 1}

f (x, y) = 7 x^{2} + 8 x y + 9 y^{2} + 9 x y^{2} + 5 x^{2} y

f (x) = (\frac{1}{x ^{3} - 2 x ^{2}}), 1 \leq x \leq \frac{7}{5}

e^{- (x^{2} + y^{2})} (x^{2} + 2 y^{2})

\frac{1}{3} x^{3} + 2 x + 4 x + 1

What is the extreme f(x)=xsqrt(1-x) ?
The extreme f(x)=xsqrt(1-x) is Maximum(2/3 , 2/(3sqrt(3))),Minimum(1,0)