What is the extreme f(x)=3xsqrt(5-x) ?

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

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extreme f(x)=3xsqrt(5-x)

extreme points

f (x) = 3 x 5 - x

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

Solution steps

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

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

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

Plug

x = 5

into

3 x 5 - x : 0

Minimum (5, 0)

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

f (x) = 2 sin (4 x)

y = - 2 sin (3 x)

f (x) = x (11 - 2 x) (13 - 2 x)

f (x) = e^{x + 1} - 5

f (x) = 4 - x^{2}

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