
Linear Approximation Consider the function
(a) Use a graphing utility to graph f. Use the zoom feature to obtain successive magnifications of the graph in the neighborhood of the point (4, 8). After zooming in a few times, the graph should appear nearly linear. Use the trace feature to determine the coordinates of a point near (4, 8). Find an equation of the secant line S(x) through the two points.
(b) Find the equation of the line
(c) Use a graphing utility to graph f and T on the same set of coordinate axes. Note that T is a good approximation of f when x is close to 4. What happens to the accuracy of the approximation as you move farther away from the point of tangency?
(d) Demonstrate the conclusion in part (c) by completing the table.
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-3 | -2 | -1 | -0.5 | -0.
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0 | |
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0.1 | 0.5 | 1 | 2 | 3 | ||
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Chapter 2 Solutions
Calculus (MindTap Course List)
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