Question

All continuous functions have derivatives.

Short answer

The answer is FALSE.

Step-by-step solution

Step 1: Explanation

While continuity implies integrability, it does not imply differentiability. It is a prerequisite to differentiability but differentiability also requires the existence of both one-sided derivates.

Example

We have encountered many examples earlier, such as \(y = \left| x \right|.y = \left| x \right|\] is continuous everywhere because the limits exist at each point x. however, at x=0 specifically, it is not differentiable because there is a sharp point on the graph. Hence the statement is False.