What is the extreme f(x)=-x^3+3x^2+9x+10 ?

The extreme f(x)=-x^3+3x^2+9x+10 is Minimum(-1,5),Maximum(3,37)

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+9x+10

extreme points

f (x) = - x^{3} + 3 x^{2} + 9 x + 10

Minimum (- 1, 5), Maximum (3, 37)

Solution steps

f^{'} (x) = - 3 x^{2} + 6 x + 9

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 1

into

- x^{3} + 3 x^{2} + 9 x + 10 : 5

Minimum (- 1, 5)

Plug

x = 3

into

- x^{3} + 3 x^{2} + 9 x + 10 : 37

Maximum (3, 37)

Minimum (- 1, 5), Maximum (3, 37)

What is the extreme f(x)=-x^3+3x^2+9x+10 ?
The extreme f(x)=-x^3+3x^2+9x+10 is Minimum(-1,5),Maximum(3,37)