A question professor couldnt solve

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The discussion revolves around whether it is possible for the limit of the derivative of a function as x approaches a point a to equal a value D, while the derivative at that point f'(a) exists but is not equal to D. Participants explore examples and mathematical properties, particularly focusing on the Darboux property, which states that derivatives have the intermediate value property. It is concluded that if f'(a) exists, then it must equal the limit of f'(x) as x approaches a, thus no such function can exist where these values differ. The consensus emphasizes that the intermediate value property for derivatives ensures continuity in this context.
  • #31
Haha. This makes me happy. I wasn't the only one making the mistake :biggrin:
 

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