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?