What is the extreme f(x)=x^4-4x^3+3 ?

The extreme f(x)=x^4-4x^3+3 is Saddle(0,3),Minimum(3,-24)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x^4-4x^3+3

extreme points

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

Saddle (0, 3), Minimum (3, - 24)

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} + 3 : 3

Saddle (0, 3)

Plug

x = 3

into

x^{4} - 4 x^{3} + 3 : - 24

Minimum (3, - 24)

Saddle (0, 3), Minimum (3, - 24)

y = \frac{2 x ^{2} + x - 6}{x ^{2} + x - 30}

f (x) = 6 x^{\frac{1}{4}} + 5

x - y = 7

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

f (x) = 3 (x + 1)^{2} - 15

What is the extreme f(x)=x^4-4x^3+3 ?
The extreme f(x)=x^4-4x^3+3 is Saddle(0,3),Minimum(3,-24)