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. Problems marked with * are to be submitted for grading. All other problems are not to be submitted but you are still encouraged to solve them for practice. 1. Consider the following graph of a function f. A HNOJH>Ul (a) On the graph above, sketch the tangent lines at a: : l, :1: : 2, x : 3, :23 : 5, and r = 7. (b) What is f'(5)? What is f'(7)? What is f'(2)? (c) For what range(s) of x values on the graph is f'(:13) negative? (d) Explain why f ' (6) does not exist, in two different ways: ( 1) by saying something about the tangent line, and (2) using the limit denition of the derivative. (Hint: Think about the one-sided limits, from the left and from the right.) (6) At what other value of CE does f ' (as) not exist