Question

For some positive constant C, a patient's temperature change, T, due to a dose, D, of a drug is given by T = (C/2 - D/3)D²

What doseage maximizes the temperature change?

Answer 1

To find the dosage that maximizes the temperature change, take the derivative of the temperature change function with respect to the dose, set it equal to zero, and solve for the dose.

Step-by-step explanation:

To find the dosage that maximizes the temperature change, we can take the derivative of the temperature change function, T, with respect to the dose, D, and set it equal to zero. This will give us the critical points where the maximum or minimum occurs.

Taking the derivative of T with respect to D, we get: T' = C - (2/3)D. Setting T' = 0 and solving for D, we find that D = (3/2)C. Substituting this value of D back into the original equation for T, we get the maximum temperature change: T = (C²/2) - (C²/3) = (C²/6).