1. ## Continuity

Is a graph continuous if it has a cusp? I believe that a graph is not differentiable at a cusp. If a graph is not differentiable at a point then it is not continuous.

2. ## Re: Continuity

If a function is not continuous, then it is not differentiable, but the converse is not true in general.

3. ## Re: Continuity

Originally Posted by IDontunderstand
Is a graph continuous if it has a cusp? I believe that a graph is not differentiable at a cusp. If a graph is not differentiable at a point then it is not continuous.
Definitions do vary.
But I think that it is generally agreed that graphs are continuous at cusps.