What is the extreme f(x)=x*sqrt(500-x) ?

The extreme f(x)=x*sqrt(500-x) is Maximum(1000/3 ,(10000sqrt(5))/(3sqrt(3))),Minimum(500,0)

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extreme f(x)=x*sqrt(500-x)

extreme

Maximum (\frac{1000}{3}, \frac{10000 5}{3 3}), Minimum (500, 0)

Solution steps

f^{'} (x) = \frac{- 3 x + 1000}{2 500 - x}

Find intervals:

Increasing

: - \infty < x < \frac{1000}{3},

Decreasing

: \frac{1000}{3} < x < 500

Plug

x = \frac{1000}{3}

into

x \cdot 500 - x : \frac{10000 5}{3 3}

Maximum (\frac{1000}{3}, \frac{10000 5}{3 3})

Plug

x = 500

into

x \cdot 500 - x : 0

Minimum (500, 0)

Maximum (\frac{1000}{3}, \frac{10000 5}{3 3}), Minimum (500, 0)

What is the extreme f(x)=x*sqrt(500-x) ?
The extreme f(x)=x*sqrt(500-x) is Maximum(1000/3 ,(10000sqrt(5))/(3sqrt(3))),Minimum(500,0)