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

The extreme f(x)=xsqrt(5-x) is Maximum(10/3 ,(10sqrt(5))/(3sqrt(3))),Minimum(5,0)

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

extreme points

f (x) = x 5 - x

Maximum (\frac{10}{3}, \frac{10 5}{3 3}), Minimum (5, 0)

Solution steps

f^{'} (x) = \frac{- 3 x + 10}{2 5 - x}

Find intervals:

Increasing

: - \infty < x < \frac{10}{3},

Decreasing

: \frac{10}{3} < x < 5

Plug

x = \frac{10}{3}

into

x 5 - x : \frac{10 5}{3 3}

Maximum (\frac{10}{3}, \frac{10 5}{3 3})

Plug

x = 5

into

x 5 - x : 0

Minimum (5, 0)

Maximum (\frac{10}{3}, \frac{10 5}{3 3}), Minimum (5, 0)

f (x) = cos (3 x) - 2, (0, 2 π)

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

f (x) = - 3 sin (2 x) - 4

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

f (x) = 2 sin^{2} (x), 0 \leq x \leq π

What is the extreme f(x)=xsqrt(5-x) ?
The extreme f(x)=xsqrt(5-x) is Maximum(10/3 ,(10sqrt(5))/(3sqrt(3))),Minimum(5,0)