Here is a problem that I am having trouble with.(adsbygoogle = window.adsbygoogle || []).push({});

Let f be a function such that:

Limit as h -->0 [f(2 + h) - f(2)] / h = 5

(essentially that: f ' (2) = 5 ).

It then asks: which of the following must be true?

1) f is continuous at x = 2.

2) f is differentiable at x = 2.

3) The derivative of f is continuous at x = 2.

THE ANSWERS: The first two are true, but the last one is false.

I understand the first two statements and how they must be true, but I also think the third statement must also be true. I can't think of an example of a function that disproves number 3. Can you?

I've tried drawing some possible functions for f ' that has a discontinuity (asymptote, jump, point) at x = 2 but whose antiderivative f is still continuous and differentiable at x = 2, but I can't come up with an example that works!

Thanks for any help

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# A question for you all

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