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

The extreme f(x)=-x^3+3x^2+9x+2 is Minimum(-1,-3),Maximum(3,29)

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+2

extreme points

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

Minimum (- 1, - 3), Maximum (3, 29)

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 + 2 : - 3

Minimum (- 1, - 3)

Plug

x = 3

into

- x^{3} + 3 x^{2} + 9 x + 2 : 29

Maximum (3, 29)

Minimum (- 1, - 3), Maximum (3, 29)

f (x) = x^{3} - 5 x^{2} + 8 x

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

(x + 1)^{5} - 5 x - 2

f (x) = \frac{2 x - 1}{x ^{2}}

f (x, y) = (2 x - x^{2}) \cdot (2 y - y^{2})

What is the extreme f(x)=-x^3+3x^2+9x+2 ?
The extreme f(x)=-x^3+3x^2+9x+2 is Minimum(-1,-3),Maximum(3,29)