en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=(x+1)^2(x-1/2)(x-2)

Solution

extreme points

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

Solution

Minimum (- 1, 0), Maximum (\frac{11 - 3 17}{16}, \frac{4131 17 - 16859}{8192} + 1), Minimum (\frac{11 + 3 17}{16}, \frac{- 16859 - 4131 17}{8192} + 1)

Solution steps

f^{'} (x) = \frac{1}{2} (x + 1) (8 x^{2} - 11 x - 1)

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < \frac{11 - 3 17}{16},

Decreasing

: \frac{11 - 3 17}{16} < x < \frac{11 + 3 17}{16},

Increasing

: \frac{11 + 3 17}{16} < x < \infty

Plug

x = - 1

into

(x + 1)^{2} (x - \frac{1}{2}) (x - 2) : 0

Minimum (- 1, 0)

Plug

x = \frac{11 - 3 17}{16}

into

(x + 1)^{2} (x - \frac{1}{2}) (x - 2) : \frac{4131 17 - 16859}{8192} + 1

Maximum (\frac{11 - 3 17}{16}, \frac{4131 17 - 16859}{8192} + 1)

Plug

x = \frac{11 + 3 17}{16}

into

(x + 1)^{2} (x - \frac{1}{2}) (x - 2) : \frac{- 16859 - 4131 17}{8192} + 1

Minimum (\frac{11 + 3 17}{16}, \frac{- 16859 - 4131 17}{8192} + 1)

Minimum (- 1, 0), Maximum (\frac{11 - 3 17}{16}, \frac{4131 17 - 16859}{8192} + 1), Minimum (\frac{11 + 3 17}{16}, \frac{- 16859 - 4131 17}{8192} + 1)

Popular Examples

extreme P(x,y)=xy extreme points

P (x, y) = x y

extreme x-2sin(x)(0.2pi)extreme points

x - 2 sin (x) (0.2 π)

extreme f(x,y)=(x+y)^{-1}extreme points

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

extreme f(x)=x^2-18x extreme points

f (x) = x^{2} - 18 x

extreme f(x,y)=sqrt(400-49x^2-16y^2)extreme points

f (x, y) = 400 - 49 x^{2} - 16 y^{2}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x+1)^2(x-1/2)(x-2) ?
The extreme f(x)=(x+1)^2(x-1/2)(x-2) is