What is the extreme f(x)=12x^2-x^3 ?

The extreme f(x)=12x^2-x^3 is Minimum(0,0),Maximum(8,256)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=12x^2-x^3

extreme points

f (x) = 12 x^{2} - x^{3}

Minimum (0, 0), Maximum (8, 256)

Solution steps

f^{'} (x) = 24 x - 3 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 8,

Decreasing

: 8 < x < \infty

Plug

x = 0

into

12 x^{2} - x^{3} : 0

Minimum (0, 0)

Plug

x = 8

into

12 x^{2} - x^{3} : 256

Maximum (8, 256)

Minimum (0, 0), Maximum (8, 256)

x^{3} - 3 x + 1, - \frac{3}{2} \leq x \leq 3

F (X, Y) = X (X + Y) + X (X + Y)

- x^{2} - 3.7 x - 6.5

f (x) = - 2 x^{3} + 33 x^{2} - 168 x + 10

f (x) = 4 x^{3} - 6 x^{2} - 144 x + 1

What is the extreme f(x)=12x^2-x^3 ?
The extreme f(x)=12x^2-x^3 is Minimum(0,0),Maximum(8,256)