Chapter 2: Q. 60 (page 185)
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The tangent line to at
Short Answer
The equation of tangent is
Chapter 2: Q. 60 (page 185)
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The tangent line to at
The equation of tangent is
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Get started for freeUse the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The tangent line to at
Prove, in two ways, that the power rule holds for negative integer powers
a) by using the definition of the derivative
b) by using thedefinition of the derivative
In Exercises 69-80, determine whether or not is continuous and/or differentiable at the given value of . If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.
For each function graphed in Exercises 65-68, determine the values of at which fails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.
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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