Let f(x)=x2−4x+1. Consider the point A on the graph where x=2.
a. (i) Find the instantaneous rate of change of f at x=2.
b. (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].
c. (iii) Determine all non–zero values of h for which the average rate obtained in (ii) equals the instantaneous rate found in (i).
d. (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.