What is the extreme f(x)=-x^3+3x^2+24x+3 ?

The extreme f(x)=-x^3+3x^2+24x+3 is Minimum(-2,-25),Maximum(4,83)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=-x^3+3x^2+24x+3

extreme points

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

Minimum (- 2, - 25), Maximum (4, 83)

Solution steps

f^{'} (x) = - 3 x^{2} + 6 x + 24

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 2

into

- x^{3} + 3 x^{2} + 24 x + 3 : - 25

Minimum (- 2, - 25)

Plug

x = 4

into

- x^{3} + 3 x^{2} + 24 x + 3 : 83

Maximum (4, 83)

Minimum (- 2, - 25), Maximum (4, 83)

What is the extreme f(x)=-x^3+3x^2+24x+3 ?
The extreme f(x)=-x^3+3x^2+24x+3 is Minimum(-2,-25),Maximum(4,83)