MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Let f(x)=x2−4x+1. Consider the point A on the graph where x=2.
(i) Find the instantaneous rate of change of f at x=2.
(ii) For a non–zero real number h, write the expression for the average rate of change of f over the interval [2,2+h].
(iii) Determine all non–zero values of h for which the average rate obtained in (ii) equals the instantaneous rate found in (i).
(iv) For each value of h obtained in (iii), state the coordinates of the second point B on the graph such that the secant line through A and B has the same slope as the tangent at A.