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Calculus/differentiation and continuity

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Question
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.

Answer
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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Calculus

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