Applied Calculus, Spring 2012
Comments on Corrections from First Exam

Here are correct answers to two of the questions from the exam.

3a:  The idea of a derivative can be related to zooming as follows.  Saying that the derivative at a point is equal to a specific number, say 2, means that if you magnify the graph far enough it will appear to become a straightline with a slope of 2, and that any additional zooming will not alter that appearance.  On the other hand, there are some graphs that will not become a straight line no matter how much you magnify them.  For these graphs there is no tangent line defined, and the derivative at such a point does not exist.

4.  The graph below shows a pretty accurate answer.  The colored lines in the top graph are lines with slope of plus or minus 2, and I estimated the maximum and minimum tangent line slopes (that is, most positive and most negative) in order to plot high and low points on the lower graph.