1. Given two real numbers (1,!) 6 IR, we dene a function f (cc) by {ME Ogscgl, aw+b, :c>1. f($) = (a) Suppose a = 2 and b = 1. Make a careful sketch of the graph of f (3:) on the interval [0, 2] and use it to argue whether or not f (93) is continuous at 5c 2 1, and whether or not f (as) is differentiable at a: = 1. (b) Suppose an) is continuous at a: = 1. Show that b = 1 a. (c) Suppose I) = 1 a. For what values of a and b is f differentiable at a: = 1? (d) Suppose f(5c) is differentiable at 1. Compute f(1.02). Use a calculator to calculate V1.02 to an accuracy of 5 decimal places. Use the notion of local linearization to explain why f (1.02) is a good estimate for V1.02