Continuity and Differentiability. 12 class math full chapter

What is the difference between continuity and differentiability?

**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.

Does continuity mean differentiability?

If f is

**differentiable**at a point x_{0}, then f must also be continuous at x_{0}. In particular, any**differentiable**function must be continuous at every point in its domain. The converse**does**not hold: a continuous function need not be**differentiable**.Does continuity imply differentiability?

**Differentiability Implies Continuity**If is a

**differentiable**function at , then is continuous at . ... If is not continuous at , then is not

**differentiable**at . Thus from the theorem above, we see that all

**differentiable**functions on are continuous on .

## No comments:

## Post a Comment