Function ##f(x)=x^4## has minimum at ##x=0##.(adsbygoogle = window.adsbygoogle || []).push({});

## f'(x)=4x^3##

##f'(0)=0##

##f''(x)=12x^2##

##f''(0)=0##

##f^{(3)}(x)=24x##

##f^{(3)}(0)=0##

##f^{(4)}(0)>0##

So what is the rule? I must go to the higher derivatives if ##f'(0)=f''(0)=0##?

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# I must go to the higher derivatives?

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