I found a statement somewhere in my notes that if we have a higher order function and lets say we take the nth derivative of it. If n is odd and the result turns out to be any number except zero then we will not be able to tell whether the curve has a maxima or a minima at that point.why is it so? What's the reason behind it?

  • $\begingroup$ Are you taking the n-th derivative and calculating it at a specific point? $\endgroup$ Jun 26, 2016 at 15:20
  • $\begingroup$ But is it necessary that if we derive it odd no. Of times getting a non zero constant at the end. Then we will not be able to tell whether it's a maxima or a minima. $\endgroup$ Jun 26, 2016 at 15:23
  • $\begingroup$ In using this at a point $c,$ I believe all the lower derivatives have to vanish at $c$ before the $n$th derivative at $c$ can give any information. $\endgroup$
    – coffeemath
    Jun 26, 2016 at 15:52


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