Mathematics, 01.04.2020 19:13 viktoria1198zz

The reaction of the body to a dose of medicine can sometimes be represented by an equation of the form RequalsUpper M squared left parenthesis StartFraction Upper C Over 2 EndFraction minus StartFraction Upper M Over 3 EndFraction right parenthesis , where C is a positive constant and M is the amount of medicine absorbed in the blood. If the reaction is a change in blood pressure, R is measured in millimeters of mercury. If the reaction is a change in temperature, R is measured in degrees, and so on. Find StartFraction dR Over dM EndFraction . This derivative, as a function of M, is called the sensitivity of the body to the medicine. Find the amount of medicine to which the body is most sensitive by finding the value of M that maximizes the derivative dR/dM.

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