The graph y = f (x) passes through the points (1, 5) and (3, 7). The tangent line to y = f (x) at (3, 7) has the equation: y = 2x + 13 [earlier there is a typo here]. Sketch a possible graph of f and the tangent line. What is the average rate of change of f (x) on the interval 1 x 3? What is the instantaneous rate of change of f (x) at the point (3, 7)? Explain. Explain why f (x) has a critical number in the interval 1 x 3? You can assume that f (x) is continuous. In your explanation use the The Mean Value Theorem, to argue that for some c, f (c) = 1. Then use the Intermediate Value Theorem applied to f (x) to argue that for some d, f (d) = 0.