What is the extreme f(x)=x(40-2x)^2 ?

The extreme f(x)=x(40-2x)^2 is Maximum(20/3 , 128000/27),Minimum(20,0)

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extreme f(x)=x(40-2x)^2

extreme points

f (x) = x (40 - 2 x)^{2}

Maximum (\frac{20}{3}, \frac{128000}{27}), Minimum (20, 0)

Solution steps

f^{'} (x) = 4 (x - 20) (3 x - 20)

Find intervals:

Increasing

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

Decreasing

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

Increasing

: 20 < x < \infty

Plug

x = \frac{20}{3}

into

x (40 - 2 x)^{2} : \frac{128000}{27}

Maximum (\frac{20}{3}, \frac{128000}{27})

Plug

x = 20

into

x (40 - 2 x)^{2} : 0

Minimum (20, 0)

Maximum (\frac{20}{3}, \frac{128000}{27}), Minimum (20, 0)

y = \frac{x}{( x - 2 ) ^{2}}

\frac{x ^{3}}{3} - \frac{3 x ^{2}}{2} + 3

f (x) = 10000 e^{0.84 (x - 1.4)^{2}}

f (x, y) = 3 x^{2} y - y

f (x, y) = x^{2} + y^{2} + x y + 3 x - 6 y + 1

What is the extreme f(x)=x(40-2x)^2 ?
The extreme f(x)=x(40-2x)^2 is Maximum(20/3 , 128000/27),Minimum(20,0)