What is the extreme f(x)=3xsqrt(x-x^2) ?

The extreme f(x)=3xsqrt(x-x^2) is Minimum(0,0),Maximum(3/4 ,(9sqrt(3))/(16)),Minimum(1,0)

Popular >

extreme f(x)=3xsqrt(x-x^2)

extreme points

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

Minimum (0, 0), Maximum (\frac{3}{4}, \frac{9 3}{16}), Minimum (1, 0)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Plug

x = 0

into

3 x x - x^{2} : 0

Minimum (0, 0)

Plug

x = \frac{3}{4}

into

3 x x - x^{2} : \frac{9 3}{16}

Maximum (\frac{3}{4}, \frac{9 3}{16})

Plug

x = 1

into

3 x x - x^{2} : 0

Minimum (1, 0)

Minimum (0, 0), Maximum (\frac{3}{4}, \frac{9 3}{16}), Minimum (1, 0)

- x^{3} - x^{2}

h (x) = 2 x^{3} - 24 x

y = x x^{2} + 1

f (x) = 4 x^{2} + y^{2}

f (x) = ln (4 x)

What is the extreme f(x)=3xsqrt(x-x^2) ?
The extreme f(x)=3xsqrt(x-x^2) is Minimum(0,0),Maximum(3/4 ,(9sqrt(3))/(16)),Minimum(1,0)