What is the extreme f(x)=x(6-2x)^2 ?

The extreme f(x)=x(6-2x)^2 is Maximum(1,16),Minimum(3,0)

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extreme f(x)=x(6-2x)^2

extreme points

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

Maximum (1, 16), Minimum (3, 0)

Solution steps

f^{'} (x) = 12 (x - 3) (x - 1)

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 1

into

x (6 - 2 x)^{2} : 16

Maximum (1, 16)

Plug

x = 3

into

x (6 - 2 x)^{2} : 0

Minimum (3, 0)

Maximum (1, 16), Minimum (3, 0)

f (x, y) = 22 x^{4} + 22 y^{4} - 4 x y + 18

f (x) = \frac{1}{4} x^{4} + \frac{1}{3} x^{3} - x^{2} + \frac{2}{3}

f (x, y) = - 4 \cdot \frac{x ^{2} + 6 x + 8}{y ^{2} + 6 y + 6}

f (x) = x + \frac{108}{x ^{2}}

f (x) = \frac{3 x ^{2}}{\frac{1}{2} x ^{2} + 1}

What is the extreme f(x)=x(6-2x)^2 ?
The extreme f(x)=x(6-2x)^2 is Maximum(1,16),Minimum(3,0)