What is the extreme f(x)=x(25-40+2x)(40/2-x) ?

The extreme f(x)=x(25-40+2x)(40/2-x) is Minimum(10/3 ,-12500/27),Maximum(15,1125)

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extreme f(x)=x(25-40+2x)(40/2-x)

extreme points

f (x) = x (25 - 40 + 2 x) (\frac{40}{2} - x)

Minimum (\frac{10}{3}, - \frac{12500}{27}), Maximum (15, 1125)

Solution steps

f^{'} (x) = - 2 (3 x - 10) (x - 15)

Find intervals:

Decreasing

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

Increasing

: \frac{10}{3} < x < 15,

Decreasing

: 15 < x < \infty

Plug

x = \frac{10}{3}

into

x (25 - 40 + 2 x) (\frac{40}{2} - x) : - \frac{12500}{27}

Minimum (\frac{10}{3}, - \frac{12500}{27})

Plug

x = 15

into

x (25 - 40 + 2 x) (\frac{40}{2} - x) : 1125

Maximum (15, 1125)

Minimum (\frac{10}{3}, - \frac{12500}{27}), Maximum (15, 1125)

f (x) = x^{\frac{1}{5}} (x + 12)

F (x, y) = x^{2} y^{2} + x^{2} y + x y^{2} + x y

f (x) = ((x - 6)^{(\frac{4}{7})}) - 3

x^{3} - 8 y^{3} + 4 x y - 8

f (x, y) = 2 x^{2} - 4 x + y^{2} - 6 y + 1

What is the extreme f(x)=x(25-40+2x)(40/2-x) ?
The extreme f(x)=x(25-40+2x)(40/2-x) is Minimum(10/3 ,-12500/27),Maximum(15,1125)