What is the extreme f(x)=x(7-x)(30-2x) ?

The extreme f(x)=x(7-x)(30-2x) is Maximum(3,288),Minimum(35/3 ,-9800/27)

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extreme f(x)=x(7-x)(30-2x)

extreme

Maximum (3, 288), Minimum (\frac{35}{3}, - \frac{9800}{27})

Solution steps

f^{'} (x) = 2 (x - 3) (3 x - 35)

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < \frac{35}{3},

Increasing

: \frac{35}{3} < x < \infty

Plug

x = 3

into

x (7 - x) (30 - 2 x) : 288

Maximum (3, 288)

Plug

x = \frac{35}{3}

into

x (7 - x) (30 - 2 x) : - \frac{9800}{27}

Minimum (\frac{35}{3}, - \frac{9800}{27})

Maximum (3, 288), Minimum (\frac{35}{3}, - \frac{9800}{27})

What is the extreme f(x)=x(7-x)(30-2x) ?
The extreme f(x)=x(7-x)(30-2x) is Maximum(3,288),Minimum(35/3 ,-9800/27)