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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 = ³ - 28. (a) Find ds/dr by implicit differentiation and evaluate it at r = 4, s = 6. [Hint: Differentiate the equation with respect to r.] ds dr = (b) Find dr/ds by implicit differentiation and evaluate it at r = 4, s = 6. [Hint: Differentiate the original equation with respect to s.] ds = (c) Interpret your answer to part (a) as a rate of change. O 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). O Changing research will not affect sales. O 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). Interpret your answer to part (b) as a rate of change. O Changing sales will not affect research. O 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). O 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).

If a company spends r million dollars on research, it sales will be s million dollars, where r and s are related by s² = ³ - 28. (a) Find ds/dr by implicit differentiation and evaluate it at r = 4, s = 6. [Hint: Differentiate the equation with respect to r.] ds dr = (b) Find dr/ds by implicit differentiation and evaluate it at r = 4, s = 6. [Hint: Differentiate the original equation with respect to s.] ds = (c) Interpret your answer to part (a) as a rate of change. O 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). O Changing research will not affect sales. O 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). Interpret your answer to part (b) as a rate of change. O Changing sales will not affect research. O 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). O 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).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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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 = 3 – 28. (a) Find ds/dr by implicit differentiation and evaluate it at r = 4, s = 6. [Hint: Differentiate the equation with respect to r.] ds dr (b) Find dr/ds by implicit differentiation and evaluate it at r = 4, s = 6. [Hint: Differentiate the original equation with respect to s.] dr ds (c) Interpret your answer to part (a) as a rate of change. 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). 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). Interpret your answer to part (b) as a rate of change. Changing sales will not affect research. 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).
Transcribed Image Text:If a company spends r million dollars on research, it sales will be s million dollars, where r and s are related by s² = 3 – 28. (a) Find ds/dr by implicit differentiation and evaluate it at r = 4, s = 6. [Hint: Differentiate the equation with respect to r.] ds dr (b) Find dr/ds by implicit differentiation and evaluate it at r = 4, s = 6. [Hint: Differentiate the original equation with respect to s.] dr ds (c) Interpret your answer to part (a) as a rate of change. 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). 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). Interpret your answer to part (b) as a rate of change. Changing sales will not affect research. 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).
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