Chapter 2: Q. 62 (page 222)
In Exercises 59–63, find a function f that has the given derivative f'. In each case you can find the answer with an educated guess-and-check process.
Short Answer
The required function is
Chapter 2: Q. 62 (page 222)
In Exercises 59–63, find a function f that has the given derivative f'. In each case you can find the answer with an educated guess-and-check process.
The required function is
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Get started for freeFor each function f and value in Exercises 35–44, use a sequence of approximations to estimate . Illustrate your work with an appropriate sequence of graphs of secant lines.
Use the definition of the derivative to find for each function in Exercises 39-54.
Every morning Linda takes a thirty-minute jog in Central Park. Suppose her distance s in feet from the oak tree on the north side of the park minutes after she begins her jog is given by the function shown that follows at the left, and suppose she jogs on a straight path leading into the park from the oak tree.
(a) What was the average rate of change of Linda’s distance from the oak tree over the entire thirty-minute jog? What does this mean in real-world terms?
(b) On which ten-minute interval was the average rate of change of Linda’s distance from the oak tree the greatest: the first minutes, the second minutes, or the lastminutes?
(c) Use the graph of to estimate Linda’s average velocity during the -minute interval from. What does the sign of this average velocity tell you in real-world terms?
(d) Approximate the times at which Linda’s (instantaneous) velocity was equal to zero. What is the physical significance of these times?
(e) Approximate the time intervals during Linda’s jog that her (instantaneous) velocity was negative. What does a negative velocity mean in terms of this physical example?
Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
27.
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