11-26-2011, 08:28 PM

Lesson 3 - Continuity

Does the derivative exist?

To text if the derivative exists, we can observe three things.

- Is the function continuous at that point?

- Are the slope before and after the point opposite? If the function forms a point (the tangent never has a slope of 0), the function is not differentiable at that point.

How do we find if the graph is continuous at a point?

A function is said to be continuous at a point (A) if:

- F is defined at A.

- The limit of f(A) exists.

- The limit of f(A) equals A.