If is differentiable on with and for all , what is the maximum possible value of ?

Answer and explanation

Correct answer: A. established via the Mean Value Theorem

  1. Step 1: By the Mean Value Theorem, there exists such that . Rearrange: . Since , . **Answer: established via the Mean Value Theorem. Why not the others:** " direct product" evaluates but forgets to add the initial value ; " additive upper" adds an extra unit without mathematical justification from the MVT; " linear bound" corresponds to a slope bound of instead of .

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