A function is said to be differentiable at a point if the limit which defines the derivate exists at that point.
Theorem Differentiability Implies Continuity. Example continued Let's calculate the limit for x at the value 0: Such a function is not a continuously differentiable. To be differentiable at a certain point, the function must first of all be defined there!
So it is not differentiable. The first two are; the third is weaker. In the former case, we sometimes have a cusp on the graph, and in the latter case, we get a point of vertical tangency.
The definition of continuously differentiable functions Ask Question.
Return to Main Page Part A: So "continuously differentiable" means "differentiable in a continuous way". ManiAm ManiAm 288 1 2 9. Because when a function is differentiable we can use all the power of calculus when working with it.