If a company spends million dollars on research, it sales

Last updated: 7/13/2022

If a company spends million dollars on research, it sales will be s million dollars, where r and s are related by s² = 3³ – 55. (a) Find ds/dr by implicit differentiation and evaluate it at r = 4, s = 3. [Hint: Differentiate the equation with respect to r.] ds/dr= (b) Find dr/ds by implicit differentiation and evaluate it at r = 4, s = 3. [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 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 r and s). Changing research will not affect sales. Interpret your answer to part (b) as a rate of change. Changing sales will not affect res 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).