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

The extreme f(x)=-2x^3+3x^2+12x+2 is Minimum(-1,-5),Maximum(2,22)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

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

Minimum (- 1, - 5), Maximum (2, 22)

Solution steps

f^{'} (x) = - 6 x^{2} + 6 x + 12

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 1

into

- 2 x^{3} + 3 x^{2} + 12 x + 2 : - 5

Minimum (- 1, - 5)

Plug

x = 2

into

- 2 x^{3} + 3 x^{2} + 12 x + 2 : 22

Maximum (2, 22)

Minimum (- 1, - 5), Maximum (2, 22)

f (x, y) = y^{3} - 3 y x^{2} - 3 y^{2} - 3 x^{2} + 1

f (x, y) = ln (\frac{1}{x + y})

f (x, y) = 4 x + 6 y

f (x) = x^{4} - 4 x^{3} + 5

x^{4} - 10 x^{2} + 9

What is the extreme f(x)=-2x^3+3x^2+12x+2 ?
The extreme f(x)=-2x^3+3x^2+12x+2 is Minimum(-1,-5),Maximum(2,22)