What is the extreme f(x)=x(15-40+2x)(40/2-x) ?

The extreme f(x)=x(15-40+2x)(40/2-x) is Minimum(5,-1125),Maximum(50/3 , 12500/27)

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extreme f(x)=x(15-40+2x)(40/2-x)

extreme

Minimum (5, - 1125), Maximum (\frac{50}{3}, \frac{12500}{27})

Solution steps

f^{'} (x) = - 2 (x - 5) (3 x - 50)

Find intervals:

Decreasing

: - \infty < x < 5,

Increasing

: 5 < x < \frac{50}{3},

Decreasing

: \frac{50}{3} < x < \infty

Plug

x = 5

into

x (15 - 40 + 2 x) (\frac{40}{2} - x) : - 1125

Minimum (5, - 1125)

Plug

x = \frac{50}{3}

into

x (15 - 40 + 2 x) (\frac{40}{2} - x) : \frac{12500}{27}

Maximum (\frac{50}{3}, \frac{12500}{27})

Minimum (5, - 1125), Maximum (\frac{50}{3}, \frac{12500}{27})

What is the extreme f(x)=x(15-40+2x)(40/2-x) ?
The extreme f(x)=x(15-40+2x)(40/2-x) is Minimum(5,-1125),Maximum(50/3 , 12500/27)