The graphs of f and f ′ are shown over the domain [−3, 6].


Graph of f decreases from the left to a sharp turn at negative 1 comma 2 and then increases to one half comma 5 and decreases to about 3 and one half comma negative 1 and increases to 6 comma 4
Graph of f

Graph of f prime decreases from the left to open circle at negative 1 comma negative 3 and jumps to another open circle at negative 1 comma 3 and decreases to about 2 comma negative 3 and increases to about 5 comma 3 and then decreases
Graph of f ′



Part A: Calculate the average rate of change of f over [−2.5, 6]. Is the instantaneous rate of change of f ever equivalent to the average rate of change of f over [−2.5, 6]? If so, how many times are they equal in the given interval? (4 points)

Part B: Estimate the equation of a tangent line at x = 2 for the graph of f. (2 points)

Part C: Find the value for each of the limit as x approaches negative 1 of the quantity f of x minus f of negative 1 all over the quantity x minus negative 1 and the limit as x approaches 3 of the quantity f of x minus f of 3 all over the quantity x minus 3 or explain why it does not exist. (4 points)