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# a. What is the physical meaning of the derivative of a function What is the graphical ISBN: 9781559536547 285

## Solution for problem r2 Chapter 1-6

Calculus: Concepts and Applications | 2nd Edition

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Problem r2

a. What is the physical meaning of the derivative of a function? What is the graphical meaning? b. For the function in Figure 1-6a, explain how f(x) is changing (increasing or decreasing, quickly or slowly) when x equals 4, 1, 3, and 5. 4 1 3 5 x f(x) Figure 1-6a c. If f(x) = 5x, find the average rate of change of f(x) from x = 2 to x = 2.1, from x = 2 to x = 2.01, and from x = 2 to x = 2.001. How close are these average rates to the instantaneous rate, 40.235947...? Do the average rates seem to be approaching this instantaneous rate as the second value of x approaches 2? Which concept of calculus is the instantaneous rate? Which concept of calculus is used to find the instantaneous rate? d. Mary Thon runs 200 m in 26 s! Her distance, d, in meters from the start at various times t, in seconds, is given in the table. Estimate her instantaneous velocity in m/s when t = 2, t = 18, and t = 24. For which time intervals did her velocity stay relatively constant? Why is the velocity at t = 24 reasonable in relation to the velocities atother times?t (s) d (m) t (s) d (m)0 0 14 892 7 16 1034 13 18 1196 33 20 1388 47 22 15410 61 24 17612 75 26 200

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##### ISBN: 9781559536547

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