The fourth derivative test

  • #1
KLscilevothma
322
0
I was given a remark and an example in my notes.

Remark: If f ''(xo)=0, then fourth derivative test

Example:
f(x)=x4
f ''(0)=0
apply the fourth derivative test
f(4)(x)=24 >0
therefore (0,0) is a minimun point

What exacly is the fourth derivative test? I can't find any resources from the internet. What if the function f(x)=x^5 ? Do we have the eighth derivative test?
 

Answers and Replies

  • #2
Brad_Ad23
502
1
I don't recall there being a 4th derivative test.
 
  • #3
On Radioactive Waves
137
0
It looks as if you're applying the second derivative test to a second derivative.
 
  • #4
mathman
Science Advisor
8,063
540
The general idea (when the first derivative is 0) is to keep taking derivatives until you get one that's not 0. If it is an odd derivative, then you've got a horizontal inflection point. If it is an even derivative, then the sign distinguishes between max (-) and min (+).
 

Suggested for: The fourth derivative test

  • Last Post
Replies
1
Views
2K
Replies
6
Views
2K
Replies
3
Views
847
  • Last Post
Replies
2
Views
792
Replies
5
Views
15K
Replies
7
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
6
Views
18K
Replies
3
Views
2K
Replies
10
Views
2K
Top