MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Consider the polynomial function f(x)=3x2−4x. Answer the following.
(i) Calculate the average rate of change of f from x=2 to x=2+h, leaving your answer in terms of h.
(ii) Determine the value of the derivative of f at x=2 by evaluating the appropriate limit of the expression obtained in part (i).
(iii) What does the numerical value found in part (ii) indicate about the behaviour of f near x=2?