What are the solution?

Problem 1: Finding Tangent Lines (60 points) A piecewise defined function g is given by the formula ux ifx ? x A partial graph of this function is given below. In this homework, we are interested in the tangent line to g(x) at x = 2. Work through the following parts to find a formula for this tangent line, or show it does not exist. In this written homework, you will use the definition of the derivative to analyze a tricky derivative. Make sure you have practiced using the definition of the derivative to make calculations. Sample problems can be found in the Ximera textbook, Ximera homework, and recitation worksheets. 8 y = g(x) i 2 3 4 a) (3 points) First let's make a guess about what we will find. Do you think the tangent line to g(x) at x = 2 will exist? Why or why not? [Briefly explain your thinking. You may refer to the given graph in your explanations. You do not need to do any calculations for this part. This is a guess, and we are more interested in your thinking than in the exact numbers.| b) (4 points) To find the tangent line, we will need the value of g'(2). Briefly explain why we need the value of g'(2) to find the tangent line to g(x) at x = 2