en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x^4-4x^3+1

Solution

extreme points

x^{4} - 4 x^{3} + 1

Solution

Saddle (0, 1), Minimum (3, - 26)

Solution steps

f^{'} (x) = 4 x^{3} - 12 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

x^{4} - 4 x^{3} + 1 : 1

Saddle (0, 1)

Plug

x = 3

into

x^{4} - 4 x^{3} + 1 : - 26

Minimum (3, - 26)

Saddle (0, 1), Minimum (3, - 26)

Popular Examples

extreme f(x,y)=(x^4-y^4)/(x^2-y^2)extreme points

f (x, y) = \frac{x ^{4} - y ^{4}}{x ^{2} - y ^{2}}

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

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

extreme f(x)=xln(x^2-y)extreme points

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

extreme y=3x^5-20x^3 extreme points

y = 3 x^{5} - 20 x^{3}

extreme F(x,y)=5xy^3-y^4+(x^2)/2 extreme points

F (x, y) = 5 x y^{3} - y^{4} + \frac{x ^{2}}{2}

Frequently Asked Questions (FAQ)

What is the extreme x^4-4x^3+1 ?
The extreme x^4-4x^3+1 is Saddle(0,1),Minimum(3,-26)