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(1 pt) The following table gives the values of the function f(x). Use this table to answer the following questions. Before attempting this problem, study the paragraph in the middle of page 98, whose title is "Improving Numerical Estimates for the Derivative". That paragraph describes how to use the average of the average rates of change over the left and right intervals to estimate derivatives of functions that are given by tables. Use that technique in this problem. Round your answers to three decimal places. X 0 0.2 0.4 0.6 0.8 1 1.2 f(x)2 6.22 6.446.66 6.88 9.1 9.32 1. Estimate f' (0.6). To do this, first compute the average rate of change of f just to the left of 0.6, i.e, the average rate of change from 0.4 to 0.6. Next,compute the average rate of change off just to right of 0.6, i.e., the average rate of change of f from 0.6 to 0.8. Then, average these two averages to get an estimate for f'(0.6). Answer: 2. Estimate f"(0.6)|by first estimating the first derivative at 0.4, 0.6, and 0.8. Specifically, proceed as follows. Use the same technique that you used in part (1) to estimate f'(0.4). Next, use this same technique to estimate f'(0.8) At this point, you will have computed the values of f'|at 0.4, 0.6, and 0.8. Reasoning in a similar manner to that used in part 1 above, use your estimates for f'(0.4), f'(0.6)|and f' (0.8) to make an estimate for f"(0.6) Answer: (1 pt) Rework problem 42 in the Chapter 2 Review problems (page 124) of your textbook using the table below instead of the table shown in your book. Year entering high school, t1982 1986 1990 1994 1998 Percent graduating, P 62 52 41 29 15 dP a) Estimate dt for the interval between 1994 and 1998. Round your answer to two decimal places. b) Which of the following best describes d-pl dt2 between 1982 and 1998? A. always negative B. changes sign C. always positive (This problem is similar to problems 10 and 11 in section 2.4 (page 113) of your textbook.) Based on the following table of values for the function w(t), answer the questions below. t 100 110 120 130 140 150 w(t) 28.2 20.6 14.5 9.6 5.3 2 a) Which of the following best describes the derivative of w(t)? A. always negative B. changes sign C. always positive b) Which of the following best describes the second derivative of w(t)p? A. changes sign B. always positive C. always negative (This problem is similar to problems 10 and 11 in section 2.4 (page 113) of your textbook.) Based on the following table of values for the function s(t)| answer the questions below. t 0 1 2 3 4 5 s(t) 98 92 83 67 47 24 a) Which of the following best describes the derivative of s(t)? A. always positive B. always negative C. changes sign b) Which of the following best describes the second derivative of s(t)? A. changes sign B. always negative C. always positive (This problem is similar to problem 19 in section 2.4 (page 114) of your text.) Use the graph shown below (which appears in the second edition of the textbook) to answer the following questions: V. (Click your mouse on the graph itself to get a bigger copy!) a) Indicate (i.e. check) all labeled points at which f(x)|and f'(x)|are both nonzero of the same sign. A. point D B. point E C. point A D. point B E. point F F. point b) Select all labeled points at which it would be possible for exactly one of f'(x)and f"(x)] to be negative. A. point E B. point B C. point D D. point E. point F F. point A
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