Do all continuous functions have antiderivatives?If not all continuous functions are differentiable, so how is it that all continuous functions have anti-derivatives?

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potamanixv · Accepted Answer

Step 1Let   I  ⊂      R   be an interval with more than one point. If   f  :  I  ⟶      R   is a continuous function, the existence of an anti-derivative of f can be proved as follows: take   a  ∈  I and define                     F        :                    I                    ⟶                              R                                          x                    ↦                                          ∫            a            x                    f          (          t          )                                d                    t          .                    Step 2Then F is a primitive of f, by the Fundamental Theorem of Calculus.You seem to find it strange that every continuous has an anti-derivative while not all continuous functions are differentiable, but it&#039;s up to you to explain what&#039;s strange about it.

Do all continuous functions have antiderivatives? If not all continuous functions

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