What is the extreme f(x)=4xsqrt(x-x^2) ?

The extreme f(x)=4xsqrt(x-x^2) is Minimum(0,0),Maximum(3/4 ,(3sqrt(3))/4),Minimum(1,0)

extreme f(x)=4xsqrt(x-x^2)

extreme points

f (x) = 4 x x - x^{2}

Minimum (0, 0), Maximum (\frac{3}{4}, \frac{3 3}{4}), Minimum (1, 0)

Solution steps

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

Find intervals:

Increasing

: 0 < x < \frac{3}{4},

Decreasing

: \frac{3}{4} < x < 1

Plug

x = 0

into

4 x x - x^{2} : 0

Minimum (0, 0)

Plug

x = \frac{3}{4}

into

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

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

Plug

x = 1

into

4 x x - x^{2} : 0

Minimum (1, 0)

Minimum (0, 0), Maximum (\frac{3}{4}, \frac{3 3}{4}), Minimum (1, 0)

x^{3} + y^{3} - 2 x y

f (x, y) = x^{3} + y^{3} + 6 x^{2} - 9 y^{2} - 4

f (x) = \frac{1}{9} (x^{4} - 4 x^{3})

f (x) = x^{3} + 2 x^{2} - x - 10

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

What is the extreme f(x)=4xsqrt(x-x^2) ?
The extreme f(x)=4xsqrt(x-x^2) is Minimum(0,0),Maximum(3/4 ,(3sqrt(3))/4),Minimum(1,0)