# The fourth derivative test

KLscilevothma
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?