What is the extreme f(x)=5xsqrt(x-x^2) ?

The extreme f(x)=5xsqrt(x-x^2) is Minimum(0,0),Maximum(3/4 ,(15sqrt(3))/(16)),Minimum(1,0)

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extreme f(x)=5xsqrt(x-x^2)

extreme

Minimum (0, 0), Maximum (\frac{3}{4}, \frac{15 3}{16}), Minimum (1, 0)

Solution steps

f^{'} (x) = \frac{5 ( - 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

5 x x - x^{2} : 0

Minimum (0, 0)

Plug

x = \frac{3}{4}

into

5 x x - x^{2} : \frac{15 3}{16}

Maximum (\frac{3}{4}, \frac{15 3}{16})

Plug

x = 1

into

5 x x - x^{2} : 0

Minimum (1, 0)

Minimum (0, 0), Maximum (\frac{3}{4}, \frac{15 3}{16}), Minimum (1, 0)

What is the extreme f(x)=5xsqrt(x-x^2) ?
The extreme f(x)=5xsqrt(x-x^2) is Minimum(0,0),Maximum(3/4 ,(15sqrt(3))/(16)),Minimum(1,0)