en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme y=x^3-3x+1

Solution

extreme points

y = x^{3} - 3 x + 1

Solution

Maximum (- 1, 3), Minimum (1, - 1)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x^{3} - 3 x + 1 : 3

Maximum (- 1, 3)

Plug

x = 1

into

x^{3} - 3 x + 1 : - 1

Minimum (1, - 1)

Maximum (- 1, 3), Minimum (1, - 1)

Popular Examples

extreme f(x)=-2x^4+8x^3-1 extreme points

f (x) = - 2 x^{4} + 8 x^{3} - 1

extreme f(x,y)=-3*x^2-2*y^2+2*x*y+1167*x+1479*y extreme points

f (x, y) = - 3 \cdot x^{2} - 2 \cdot y^{2} + 2 \cdot x \cdot y + 1167 \cdot x + 1479 \cdot y

extreme f(x,y)=x^2+y^2+ln(xy-2)extreme points

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

extreme f(x)=2sqrt(x)e^{-x}extreme points

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

extreme f(x)=-x^4+50x^2-625,-6<= x<= 6 extreme points

f (x) = - x^{4} + 50 x^{2} - 625, - 6 \leq x \leq 6

Frequently Asked Questions (FAQ)

What is the extreme y=x^3-3x+1 ?
The extreme y=x^3-3x+1 is Maximum(-1,3),Minimum(1,-1)