What is the extreme f(x)=x^3+6x^2 ?

The extreme f(x)=x^3+6x^2 is Maximum(-4,32),Minimum(0,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x^3+6x^2

extreme points

f (x) = x^{3} + 6 x^{2}

Maximum (- 4, 32), Minimum (0, 0)

Solution steps

f^{'} (x) = 3 x^{2} + 12 x

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 4

into

x^{3} + 6 x^{2} : 32

Maximum (- 4, 32)

Plug

x = 0

into

x^{3} + 6 x^{2} : 0

Minimum (0, 0)

Maximum (- 4, 32), Minimum (0, 0)

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

f (x) = x^{3} - 27 x + 57

(6, - 2), (- 2, 3)

f (x) = \frac{x}{12}

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

What is the extreme f(x)=x^3+6x^2 ?
The extreme f(x)=x^3+6x^2 is Maximum(-4,32),Minimum(0,0)