Chapter 2: Q. 22 (page 197)
If possible, find constants a and b so that the function f that follows is continuous and differentiable everywhere. If it is not possible, explain why not.
Chapter 2: Q. 22 (page 197)
If possible, find constants a and b so that the function f that follows is continuous and differentiable everywhere. If it is not possible, explain why not.
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Get started for freeFind the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
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.
Use the definition of the derivative to find for each function f in Exercises 39-54
In Exercises 69–80, determine whether or not f is continuous and/or differentiable at the given value of x. If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.
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 .
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