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Remark: If f ''(x

_{o})=0, then fourth derivative test

Example:

f(x)=x

^{4}

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?