If a company spends rmillion dollars on research, it sales will be 5 million dollars, where rand s are related by s2 = r3 7 28. (a) Find dsldr by implicit differentiation and evaluate it atr : 4, s : 6. [Hints Differentiate the equation with respect to r.] d5 , S W (b) Find dr/ds by implicit differentiation and evaluate it at r = 4, s = 6 [Hint Differentiate the original equation with respect to 5.] L: d5 (c) Interpret your answer to part (a) as a rate of change. 0 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) 0 Changing research will not affect sales 0 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. 0 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 rn million dollars (at these levels of r and s). 0 Changing sales will not affect research 0 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 in million dollars (at these levels of r and s)' The crash risk of an intoxicated driver relative to a similar driver with zero blood alcohol is R(x) = 51500x4.14 + 1.09 where x is the blood alcohol level as a percent (0.01 s x 5 0.15). Find and compare dR and AR for x = 0.08 and dx = Ax = 0.007. [Note: x 2 0.08 defines "driving while intoxicated" and R(0.08) = 2.6 means that such a driver is 2.6 times more likely to be involved in an accident than a similar driver who is not impaired. It dR = 0.3832 X AR = -0.42 XThe reproduction function for a whale is estimated to be f(p) = -0.0005p2 + 1.02p, where p and f(p) are in thousands. Find the population that gives the maximum sustainable yield, and the size of the yield. population thousand whales size of the yield thousand whales