What is the extreme f(x)=x[36-2(x)]^2 ?

The extreme f(x)=x[36-2(x)]^2 is Maximum(6,3456),Minimum(18,0)

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extreme f(x)=x[36-2(x)]^2

extreme points

f (x) = x [36 - 2 (x)]^{2}

Maximum (6, 3456), Minimum (18, 0)

Solution steps

f^{'} (x) = 12 (x - 6) (x - 18)

Find intervals:

Increasing

: - \infty < x < 6,

Decreasing

: 6 < x < 18,

Increasing

: 18 < x < \infty

Plug

x = 6

into

x [36 - 2 x]^{2} : 3456

Maximum (6, 3456)

Plug

x = 18

into

x [36 - 2 x]^{2} : 0

Minimum (18, 0)

Maximum (6, 3456), Minimum (18, 0)

f (x) = x + 12 - 8

f (x, y) = 4 x y + 120 y - 20 y^{2} - \frac{1}{10} x^{2} y - 90

f (x, y) = 2 x^{2} + 4 y^{2} - 2 x y - 10 x - 2 y + 2

f (x) = \frac{7 x}{x ^{2} + 9}, 0 \leq x \leq 9

2 x^{3} + 4 x^{2} - 1

What is the extreme f(x)=x[36-2(x)]^2 ?
The extreme f(x)=x[36-2(x)]^2 is Maximum(6,3456),Minimum(18,0)