The fourth derivative test

  • #1

Main Question or Discussion Point

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
499
1
I don't recall there being a 4th derivative test.
 
  • #3
It looks as if you're applying the second derivative test to a second derivative.
 
  • #4
mathman
Science Advisor
7,800
430
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 (+).
 

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