Discussion The discussion items below should be answered in your own words, using verbal explanation interspersed with mathematical work. 1. Relate average rate of change to the limit definition of the derivative: f' (a ) = lim f(ath)- f(a) (A) What h new kind of rate of change (i.e., not average) does the derivative output? (B) Sketch a graph of a generic, non- linear function y = f (x ) and illustrate on the same graph (C) the left side of the equation above and (D) the right side without the limit. (4 points)2. Use your work from Question 1 to state and justify the units of f(x) . (4 points) 3. Explain why a limit is necessary to calculate the value of the derivative. (i.e., why can't we just use the average rate of change formula, as is, to get an instantaneous rate of change?) (3 points) 4. Consider the function g(x) = x +2 at x =0. Provide a table of inputs and outputs as described in class that demonstrate the limit definition of the derivative, numerically. Circle your final answer. (4 points)