What is the extreme f(x)=x*sqrt(4-x) ?

The extreme f(x)=x*sqrt(4-x) is Maximum(8/3 ,(16)/(3sqrt(3))),Minimum(4,0)

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extreme f(x)=x*sqrt(4-x)

extreme points

f (x) = x \cdot 4 - x

Maximum (\frac{8}{3}, \frac{16}{3 3}), Minimum (4, 0)

Solution steps

f^{'} (x) = \frac{- 3 x + 8}{2 4 - x}

Find intervals:

Increasing

: - \infty < x < \frac{8}{3},

Decreasing

: \frac{8}{3} < x < 4

Plug

x = \frac{8}{3}

into

x \cdot 4 - x : \frac{16}{3 3}

Maximum (\frac{8}{3}, \frac{16}{3 3})

Plug

x = 4

into

x \cdot 4 - x : 0

Minimum (4, 0)

Maximum (\frac{8}{3}, \frac{16}{3 3}), Minimum (4, 0)

What is the extreme f(x)=x*sqrt(4-x) ?
The extreme f(x)=x*sqrt(4-x) is Maximum(8/3 ,(16)/(3sqrt(3))),Minimum(4,0)