Question

How to know if a function is differentiable on an interval.

A) Discontinuous points
B) Sharp corners
C) Vertical asymptotes
D) Horizontal asymptotes

Answer 1

To know if a function is differentiable on an interval, we check for continuity, sharp corners, vertical asymptotes, and horizontal asymptotes.

Step-by-step explanation:

To determine if a function is differentiable on an interval, we need to check for several conditions:

1. The function must be continuous on the interval, meaning there are no abrupt jumps or holes in the graph (Part A).
2. The function must not have any sharp corners or cusps (Part B).
3. The function must not have any vertical asymptotes, where the graph approaches infinity or negative infinity (Part C).
4. The function must not have any horizontal asymptotes, where the graph levels off towards a specific value as x approaches infinity or negative infinity (Part D).