Question

Converse: The differentiability of f is sufficient for what?

1) Proving the continuity of f
2) Determining the limits of f
3) Finding the derivative of f
4) Establishing the integrability of f

Answer 1

The differentiability of a function f is sufficient to prove the continuity of f. Differentiability implies continuity but does not directly determine limits, find derivatives, or establish integrability.

Step-by-step explanation:

The differentiability of a function f is sufficient to prove the continuity of f. This is because if a function is differentiable at a point, it must also be continuous at that point. Differentiability implies continuity but not vice versa; some functions are continuous but not differentiable. However, differentiability does not necessarily determine the limits of f, find its derivative (since we assume the derivative exists in the context of differentiability), or establish the integrability of f. While a differentiable function is integrable, the property of being differentiable alone does not provide sufficient information on how to integrate the function.