81 88 require the following discussion of a secant line.

Chapter 2, Problem 81

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81 88 require the following discussion of a secant line. The slope of the secant line containing the two points (x, f(x)) and 1x + h, f1x + h22 on the graph of a function y = f1x2 may be given as msec = f1x + h2 - f1x2 1x + h2 - x = f1x + h2 - f1x2 h h 0 In calculus, this expression is called the difference quotient of f. (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find msec for h = 0.5, 0.1, and 0.01 at x = 1. What value does msec approach as h approaches 0? (c) Find the equation for the secant line at x = 1 with h = 0.01. (d) Use a graphing utility to graph f and the secant line found in part (c) on the same viewing window.