Chapter 2: Q. 62 (page 185)
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
The equation of tangent line is
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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 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.
For 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 the equations of the lines described in Exercises 59-64.
The line that passes through the point and is parallel to the tangent line to at .
Use the definition of the derivative to find for each function in Exercises 39-54.
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