The fourth derivative test

  • #1
KLscilevothma
314
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
136
0
It looks as if you're applying the second derivative test to a second derivative.
 
  • #4
mathman
Science Advisor
8,056
539
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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