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Calculus/differentiation and continuity


Hello sir,,I'm currently in 12th grade and I've encountered a very basic question which I'm not able to solve,,it is a theoretical question not any problem.
If a function f(x) is not derivable at a point ,, can we say that f'(x) is not continuous at that point?
If not always,,when can we say that and what about its vice-versa statement?
Thank you.

Hi Apoorv,
Differentiability implies continuity but the opposite statement doesn't hold. This means that a function can be continuous at a point where it is not differentiable, but if we know a point where it is differentiable then we can be sure it is continuous there. For instance, the function f(x) = |x| is continuous at x = 0 but isn't differentiable there.



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Ahmed Salami


I can provide good answers to questions dealing in almost all of mathematics especially from A`Level downwards. I believe i would be very helpful in calculus and can as well help a good deal in Physics with most emphasis directed towards mechanics.


Aspiring theoretical physicist. I have been doing maths and physics all my life.

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