the reaction r of the body to a dose m of medication is often represented by the general function r(m)=m^2(c…

the reaction r of the body to a dose m of medication is often represented by the general function r(m)=m^2(c - \\frac{m}{3}), where c is a constant. if the reaction is a change in blood - pressure, r is measured in millimeters of mercury (mmhg). if the reaction is a change in temperature, r is measured in degrees fahrenheit (°f). the rate of change \\frac{dr}{dm} is defined to be the bodys sensitivity to the medication. find a formula for the sensitivity. \\frac{dr}{dm}=□

the reaction r of the body to a dose m of medication is often represented by the general function r(m)=m^2(c - \\frac{m}{3}), where c is a constant. if the reaction is a change in blood - pressure, r is measured in millimeters of mercury (mmhg). if the reaction is a change in temperature, r is measured in degrees fahrenheit (°f). the rate of change \\frac{dr}{dm} is defined to be the bodys sensitivity to the medication. find a formula for the sensitivity. \\frac{dr}{dm}=□

Answer

Explanation:

Step1: Differentiate $R(M)$

Given $R(M)=M^2\left(C - \frac{M}{3}\right)=CM^2-\frac{1}{3}M^3$. Using power - rule $\frac{d}{dM}(x^n)=nx^{n - 1}$, we have $\frac{dR}{dM}=2CM - M^2$.

Answer:

$2CM - M^2$