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Chapter 2: Q. 57 (page 185)
Use the definition of the derivative to find the derivatives described in Exercises 55-58.
Givenfindand
The value is
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Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The line tangent to the graph of at the point
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鈥檚 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鈥檚 distance from the oak tree the greatest: the first minutes, the second minutes, or the lastminutes?
(c) Use the graph of to estimate Linda鈥檚 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鈥檚 (instantaneous) velocity was equal to zero. What is the physical significance of these times?
(e) Approximate the time intervals during Linda鈥檚 jog that her (instantaneous) velocity was negative. What does a negative velocity mean in terms of this physical example?
Instead of choosing small values of h, we could have chosen values of z close to c. What limit involving z instead of h is equivalent to the one involving h?
Differentiation review: Without using the chain rule find the derivative of each of the function f that follows some algebra may be required before differentiating
Use the definition of the derivative to find for each function in Exercises 34-59
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