Chapter 2: Q. 58 (page 210)
Suppose that r is an independent variable, s is a function of r, and q is a constant. Calculate the derivatives in Exercises 53– 58. Your answers may involve r, s, q, or their derivatives.
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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.
Write down a rule for differentiating a composition of four functions
(a) in “prime” notation and
(b) in Leibniz notation.
Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra
Prove the difference rule in two ways
a) using definition of the derivative
b) using sum and constant multiple rules
A tomato plant given ounces of fertilizer will successfully bear pounds of tomatoes in a growing season.
(a) In real-world terms, what does represent and what are its units? What does represent and what are its units?
(b) A study has shown that this fertilizer encourages tomato production when less than ounces are used, but inhibits production when more than ounces are used. When is positive and when is negative? When is positive and when is negative?
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