What is the extreme f(x)=x(5-x)(8-x) ?

The extreme f(x)=x(5-x)(8-x) is Maximum(2,36),Minimum(20/3 ,-400/27)

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extreme f(x)=x(5-x)(8-x)

extreme

Maximum (2, 36), Minimum (\frac{20}{3}, - \frac{400}{27})

Solution steps

f^{'} (x) = (x - 2) (3 x - 20)

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < \frac{20}{3},

Increasing

: \frac{20}{3} < x < \infty

Plug

x = 2

into

x (5 - x) (8 - x) : 36

Maximum (2, 36)

Plug

x = \frac{20}{3}

into

x (5 - x) (8 - x) : - \frac{400}{27}

Minimum (\frac{20}{3}, - \frac{400}{27})

Maximum (2, 36), Minimum (\frac{20}{3}, - \frac{400}{27})

What is the extreme f(x)=x(5-x)(8-x) ?
The extreme f(x)=x(5-x)(8-x) is Maximum(2,36),Minimum(20/3 ,-400/27)