[Math] Maximum and minimum inflection points

calculus

Theres these two related questions that are just mind boggling and I have no idea how to answer them…

  1. What is the minimum number of inflection points that must exist between (and not at ) two critical points of a non-constant differentiable polynomial?

  2. What is the maximum number of inflection points that can exist between two critical points of a differentiable function?

Best Answer

We have to stress that critical points are not counted. Also, note than a critical point is an inflection point iff it is in between one maximum point and one minimum point. Than we have:

  1. The minimum number of inflection points is 0, because the critical points may not be of the form max-min.
  2. Only one.
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