What is the extreme f(x)=x(12-2x)^2 ?

The extreme f(x)=x(12-2x)^2 is Maximum(2,128),Minimum(6,0)

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extreme f(x)=x(12-2x)^2

extreme points

f (x) = x (12 - 2 x)^{2}

Maximum (2, 128), Minimum (6, 0)

Solution steps

f^{'} (x) = 12 (x - 6) (x - 2)

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 2

into

x (12 - 2 x)^{2} : 128

Maximum (2, 128)

Plug

x = 6

into

x (12 - 2 x)^{2} : 0

Minimum (6, 0)

Maximum (2, 128), Minimum (6, 0)

f (x, y) = 8 x^{3} + y^{3} + 6 x y

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

g (x, y) = x y

f (x, y) = x^{3} + y^{3} - 3 x - 12 y + 20

f (x) = x^{3} - 6 x^{2} + 5, - 3 \leq x \leq 5

What is the extreme f(x)=x(12-2x)^2 ?
The extreme f(x)=x(12-2x)^2 is Maximum(2,128),Minimum(6,0)