Continuity and differentiability

1. How is continuity related to differentiability?
2. What is continuity and differentiation?
3. How do you know if its continuous or differentiable?

How is continuity related to differentiability?

We see that if a function is differentiable at a point, then it must be continuous at that point. There are connections between continuity and differentiability. Differentiability Implies Continuity If is a differentiable function at , then is continuous at . ... If is not continuous at , then is not differentiable at .

What is continuity and differentiation?

Continuity of a function is the characteristic of a function by virtue of which, the graphical form of that function is a continuous wave. A differentiable function is a function whose derivative exists at each point in its domain.

How do you know if its continuous or differentiable?

If f is differentiable at x=a, then f is continuous at x=a. Equivalently, if f fails to be continuous at x=a, then f will not be differentiable at x=a. A function can be continuous at a point, but not be differentiable there.