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^3+3x^2+2x

Solution

extreme points

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

Solution

Maximum (- \frac{3 + 1}{3}, 23 + \frac{- 12 3 - 16}{3 3} + 4), Minimum (\frac{- 3 + 3}{3}, - 23 + \frac{16 - 12 3}{3 3} + 4)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

: \frac{1}{3} - 1 < x < \infty

Plug

x = - \frac{3 + 1}{3}

into

x^{3} + 3 x^{2} + 2 x : 23 + \frac{- 12 3 - 16}{3 3} + 4

Maximum (- \frac{3 + 1}{3}, 23 + \frac{- 12 3 - 16}{3 3} + 4)

Plug

x = \frac{- 3 + 3}{3}

into

x^{3} + 3 x^{2} + 2 x : - 23 + \frac{16 - 12 3}{3 3} + 4

Minimum (\frac{- 3 + 3}{3}, - 23 + \frac{16 - 12 3}{3 3} + 4)

Maximum (- \frac{3 + 1}{3}, 23 + \frac{- 12 3 - 16}{3 3} + 4), Minimum (\frac{- 3 + 3}{3}, - 23 + \frac{16 - 12 3}{3 3} + 4)

Popular Examples

extreme f(x)=2x^3-21x^2+60x,1<= x<= 6 extreme points

f (x) = 2 x^{3} - 21 x^{2} + 60 x, 1 \leq x \leq 6

extreme y^3+6x^2y-6x^2-6y^2+3 extreme points

y^{3} + 6 x^{2} y - 6 x^{2} - 6 y^{2} + 3

extreme T(x,y)=100+x(y+1)^2-6x^2-8(y+1)^2 extreme points

T (x, y) = 100 + x (y + 1)^{2} - 6 x^{2} - 8 (y + 1)^{2}

extreme ((x^3))/((x-1)^2)extreme points

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

extreme f(x)=x^{1/7}+3 extreme points

f (x) = x^{\frac{1}{7}} + 3

Frequently Asked Questions (FAQ)

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