Question

In session one : Introduction to derivatives, the professor solved the example. f(x) = f(1/x) in the first 15 mins. Can anyone please explain the concept of continuity used in that example.

Answer 1

1/x is not continuous (not defined) at x=0, so the derivative is not continuous at x=0 (also not defined, I guess)...what brought up your question, I mean, why you need to concern continuity in session one, which is most probably about definition only...

Answer 2

continuity means:
LHS limit=Function value at given point x=0 =RHS limit

here value at point X=0 is 1/0 which is infinity.
So as per definition the function is not continuous at point x=0.

And if function is not continuous at a given point then it will never be differentiable.

Rule for a function to be differentiable at any point:
LHS limit = RHS limit (of f'(x))