What is the extreme x^4+2x^3-3x^2-4x+4 ?

The extreme x^4+2x^3-3x^2-4x+4 is Minimum(-2,0),Maximum(-1/2 , 81/16),Minimum(1,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x^4+2x^3-3x^2-4x+4

extreme points

x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 4

Minimum (- 2, 0), Maximum (- \frac{1}{2}, \frac{81}{16}), Minimum (1, 0)

Solution steps

f^{'} (x) = 4 x^{3} + 6 x^{2} - 6 x - 4

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 2

into

x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 4 : 0

Minimum (- 2, 0)

Plug

x = - \frac{1}{2}

into

x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 4 : \frac{81}{16}

Maximum (- \frac{1}{2}, \frac{81}{16})

Plug

x = 1

into

x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 4 : 0

Minimum (1, 0)

Minimum (- 2, 0), Maximum (- \frac{1}{2}, \frac{81}{16}), Minimum (1, 0)

f (x) = 6 x - 38

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

f (x) = x^{2} ln (\frac{x}{4})

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

What is the extreme x^4+2x^3-3x^2-4x+4 ?
The extreme x^4+2x^3-3x^2-4x+4 is Minimum(-2,0),Maximum(-1/2 , 81/16),Minimum(1,0)