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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.