Chapter 2: Q. 63 (page 185)
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 .
Short Answer
The equation is
Chapter 2: Q. 63 (page 185)
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 .
The equation is
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Get started for freeEach graph in Exercises 31โ34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.
For each function f that follows find all the x-values in the domain of f for which and all the values for which does not exist in later section we will call these values the critical points of f
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Differentiate in three ways. When you have completed all three parts, show that your three answers are the same:
(a) with the chain rule
(b) with the product rule but not the chain rule
(c) without the chain or product rules.
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.
Each graph in Exercises 31โ34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.
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