company spends r million dollars on research, it sales will be s million dollars, where r and s are related by s2=r3−28.

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Company Spends R Million Dollars On Research It Sales Will Be S Million Dollars Where R And S Are Related By S2 R3 28 1 (586.97 KiB) Viewed 41 times

company spends r million dollars on research, it sales will be s million dollars, where r and s are related by s2=r3−28. (a) Find ds/dr by implicit differentiation and evaluate it at r=4,s=6. [Hint: Differentiate the equation with respect to r.] drds​= (b) Find dr/ds by implicit differentiation and evaluate it at r=4,s=6. [Hint: Differentiate the original equation with respect to s. ) dsdr​= (c) Interpret your answer to part (a) as a rate of change. 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 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 research expenditures with respect to sales is m, so that increasing sales million dollars will increase research by about m million dollars (at these levels of r and s ). 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 ).