Question

The reaction of the body to a dose of medicine can sometimes be represented by an equation of the formR = M^2 (C/2- M/3),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 dR/dM. This derivative, as a function of M, is called the sensitivity of the body to the medicine.

Answer 1

Answer:

The derivative is $\frac{dR}{dM} = CM - M^2$

Step-by-step explanation:

From the question we are told that

The equation representing the reaction is $R = M^2 (\frac{C}{2} - \frac{M}{3} )$

Generally this equation can be represented as

$R = \frac{C M^2}{2} - \frac{M^3}{3}$

Generally $\frac{dR}{dM}$ as a function of M is mathematically represented as

$\frac{dR}{dM} = 2 * \frac{C M^{2 - 1 }}{2} + 3 * \frac{M^{3-1}}{3}$

=> $\frac{dR}{dM} = CM - M^2$