Fermat's theorem says that if is differentiable at an interior point where it has a local extremum, then . Which example shows that the converse is false?

Answer and explanation

Correct answer: A. at , where but there is no extremum

  1. Step 1: A counterexample needs without an extremum. For the derivative is at 0, yet is increasing across 0. **Answer: at , where but there is no extremum. Why not the others:** The other examples either have an extremum or do not have .

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