All differentiable functions are continuous. However, not all continuous functions are differentiable.

Naeema F.

asked • 06/08/20# Is it true that there is a function that is differentiable at x= -2, but not continuous at x = -2?

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## 2 Answers By Expert Tutors

No, differentiability implies continuity.

I am not sure why this answer was censored since it is precisely correct.

Any function which has a derivative at a point is continuous at that point.

You can easily prove this with the Mean Value Theorem.

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