Another way to approximate derivatives is to use the

Chapter 3, Problem 65

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Another way to approximate derivatives is to use the centered difference quotient: f _1a2 _ f 1a + h2 - f 1a - h2 2h . Again, consider f 1x2 = 1x. a. Graph f near the point 14, 22 and let h = 12 in the centered difference quotient. Draw the line whose slope is computed by the centered difference quotient and explain why the centered difference quotient approximates f _142. b. Use the centered difference quotient to approximate f _142 by completing the following table. c. Explain why it is not necessary to use negative values of h in the table in part (b). d. Compare the accuracy of the derivative estimates in part (b) with those found in Exercise 64.

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