Relative extrema, critical numbers, and Fermat's Theorem

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Introduction to the notion of critical numbers of a function (i.e., arguments at which the derivative of the function is either zero or undefined) and Fermat's Theorem, which asserts that relative extrema always occur at a critical number. The video includes a calculation of the critical numbers of f(x) = x^(2/3)(x-2).
  1. Chris Odden
  2. critical numbers
  3. relative extreme
  4. fermat's theorem
  5. calculus
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at 4:05 you make the claim that the average rate of change between x and c can be <= 0. This does make sense to me since that would only work if x = c which is undefined. Shouldn't it be only be strictly less than? Is there a flaw in my logic?

theflaggeddragon