Problem requires the following discussion of a secant line. The slope of the secant line containing the two points (x, f (x)) and (x + h, f (x + h)) on the graph of a function y = f (x) may be given as

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 m_sec for h = 0.5, 0.1, and 0.01 at x = 1. What value does m_sec approach ash 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.

f(x) = x² + 2x

Transcribed Image Text:

f(x + h) – f(x) (x + h) – x f(x+ h) – f(x) h + 0 msec