Answered: If a company spends r million dollars…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 8CR

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If a company spends r million dollars on research, it sales will be s million dollars, where r and s are related by

s² = r³ − 55.

(a) Find ds/dr by implicit differentiation and evaluate it at r = 4, s = 3. [Hint: Differentiate the equation with respect to r.]

(b) Find dr/ds by implicit differentiation and evaluate it at r = 4, s = 3. [Hint: Differentiate the original equation with respect to s.]

Changing research will not affect sales.Given ds/dr = n, this means that the rate of change of sales with respect to research expenditures is n, so that increasing research by one million dollars will increase sales by about n million dollars (at these levels of r and s). Given ds/dr = n, this means that the rate of change of research expenditures with respect to sales is n, so that increasing sales by one million dollars will increase research by about n million dollars (at these levels of r and s).

Interpret your answer to part (b) as a rate of change.

Given dr/ds = m, this means that the rate of change of sales with respect to research expenditures is n, so that increasing research by one million dollars will increase sales by about m million dollars (at these levels of r and s).Given dr/ds = m, this means that the rate of change of research expenditures with respect to sales is m, so that increasing sales by one million dollars will increase research by about m million dollars (at these levels of r and s). Changing sales will not affect research.

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If a company spends r million dollars on research, it sales will be s million dollars, where r and s are related by s2 = r3 − 55.