Chapter 2: Q. 30 (page 233)
Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra.
Short Answer
The derivative of the given function is: 1.
Chapter 2: Q. 30 (page 233)
Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra.
The derivative of the given function is: 1.
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Get started for freeIf Katie walked at miles per hour for minutes and then sprinted at miles an hour for minutes, how fast would Dave have to walk or run to go the same distance as Katie did at the same time while moving at a constant speed? Sketch a graph of Katie’s position over time and a graph of Dave’s position over time on the same set of axes.
Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
For each function and interval in Exercises , use the Intermediate Value Theorem to argue that the function must have at least one real root on . Then apply Newton’s method to approximate that root.
The following reciprocal rules tells us hoe to differentiate the reciprocal of a function
Prove this using
a) definition of the derivative
b) by using the quotient rule
The total yearly expenditures by public colleges and universities from 1990 to 2000 can be modeled by the function , where expenditures are measured in billions of dollars and time is measured in years since 1990.
(a) Estimate the total yearly expenditures by these colleges and universities in 1995.
(b) Compute the average rate of change in yearly expenditures between 1990 and 2000.
(c) Compute the average rate of change in yearly expenditures between 1995 and 1996.
(d) Estimate the rate at which yearly expenditures of public colleges and universities were increasing in 1995.
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