en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x^3-3x^2-5x-5

Solution

extreme points

x^{3} - 3 x^{2} - 5 x - 5

Solution

Maximum (\frac{3 - 2 6}{3}, \frac{36 - 4 6}{9} + 46 - 16), Minimum (\frac{3 + 2 6}{3}, \frac{36 + 4 6}{9} - 16 - 46)

Solution steps

f^{'} (x) = 3 x^{2} - 6 x - 5

Find intervals:

Increasing

: - \infty < x < - \frac{2 2}{3} + 1,

Decreasing

: - \frac{2 2}{3} + 1 < x < \frac{2 2}{3} + 1,

Increasing

: \frac{2 2}{3} + 1 < x < \infty

Plug

x = \frac{3 - 2 6}{3}

into

x^{3} - 3 x^{2} - 5 x - 5 : \frac{36 - 4 6}{9} + 46 - 16

Maximum (\frac{3 - 2 6}{3}, \frac{36 - 4 6}{9} + 46 - 16)

Plug

x = \frac{3 + 2 6}{3}

into

x^{3} - 3 x^{2} - 5 x - 5 : \frac{36 + 4 6}{9} - 16 - 46

Minimum (\frac{3 + 2 6}{3}, \frac{36 + 4 6}{9} - 16 - 46)

Maximum (\frac{3 - 2 6}{3}, \frac{36 - 4 6}{9} + 46 - 16), Minimum (\frac{3 + 2 6}{3}, \frac{36 + 4 6}{9} - 16 - 46)

Popular Examples

extreme f(x)= 1/3 x^3+1/2 x^2-2x+1 extreme points

f (x) = \frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 2 x + 1

extreme f(x)= 1/3 x^3+1/2 x^2-2x+2 extreme points

f (x) = \frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 2 x + 2

extreme f(x)=4x^5+25x^4-40x^3-1 extreme points

f (x) = 4 x^{5} + 25 x^{4} - 40 x^{3} - 1

extreme f(x,y)=6xy extreme points

f (x, y) = 6 x y

extreme f(x)=xsqrt(x^2+25),-6<= x<= 4 extreme points

f (x) = x x^{2} + 25, - 6 \leq x \leq 4

Frequently Asked Questions (FAQ)

What is the extreme x^3-3x^2-5x-5 ?
The extreme x^3-3x^2-5x-5 is