TITLE: What is the difference between "differentiable" and "continuous"
QUESTION [7 upvotes]: I have always treated them as the same thing. But recently, some people have told me that the two terms are different. So now I am wondering,

What is the difference between "differentiable" and "continuous"?

I just don't want to say the wrong thing. For example, I don't want to say, "$\frac{x^2}{x^4-2x^3}$ is not differentiable at $x=0$" when really, it should be "discontinuous". Please help

REPLY [2 votes]: Differentiability means that the function has a derivative at a point. 
Continuity means that the limit from both sides of a value is equal to the function's value at that point.