Question

Which of the following is true?

(a) Differentiability does not imply continuity

(b) Differentiability implies continuity

(c) Continuity implies differentiability

(d) There is no relation between continuity and differentiable

I had been asked this question in an internship interview.

I need to ask this question from Differentiability topic in division Complex Function Theory of Engineering Mathematics

Answer 1

The correct answer is (b) Differentiability implies continuity

To explain: Any function that is differentiable is definitely continuous. If a function is not continuous, it cannot be differentiable either. However, continuity cannot always imply differentiability. Sometimes, functions that are continuous are not differentiable.