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1. Consider the following graph of a function f. A ILNJOJr-bU'Ch (a) On the graph above, sketch the tangent lines at CC = 1, :19 = 2, CE = 3, :19 = 5, and :6 : 7. (b) What is f'(5)? What is f'(7)? What is f'(2)? (c) For what range(s) of :15 values on the graph is f'(a;) 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.) (e) At what other value of 1' does f ' (3:) not exist? 2. For the following functions f (x) compute the derivative f ' (1:) by using the limit denition f'(:c) = 11mm f