AP Calculus AB : Geometric understanding of graphs of continuous functions

Example Questions

Example Question #1 : Functions, Graphs, And Limits

is differentiable for which of the following values of

Explanation:

is not differentiable at  and  because the values are discontinuities.  is not differentiable at  because that point is a corner, indicating that the one-side limits at  are different.  is differentiable:the one side limits are the same and the point is continuous.

Example Question #2 : Continunity As A Property Of Functions

Consider the graph of  above. What can we say about  when  ?

has a horizontal tangent at .

None of these are correct.

is discontinuous at  because there is a sharp turn at .

Two or more of these are correct.

has a removable discontinuity at .