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HOW DO YOU SEE IT? Use the graph of f to answer each question. To print an enlarged copy of the graph, go to MathGraphs.com.
(a) Between which two consecutive points is the average rate of change of the function greatest?
(b) Is the average rate of change of the function between A and B greater than or less than the instantaneous rate of change at B?
(c) Sketch a tangent line to the graph between C and D such that the slope of the tangent line is the same as the average rate of change of the function between C and D.
Secant Lines Consider the function and the point P (4, 2) on the graph of f.
(a) Graph f and the secant lines passing through P (4, 2) and Q(x, f(x)) for x-values of 1, 3, and 5.
(b) Find the slope of each secant line.
(c) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P (4, 2). Describe how to improve your approximation of the slope.