# Calculus

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24. A pharmaceutical company has determined that a realistic model for the relationship between blood pressure (systolic) and the amount of a nerve drug designed to reduce the systolic pressure is given by the equation P=Pi + 2x - x^2.
P is measured in millimeters of mercury and x is the number of milligrams of the drug administered 30 minutes before the reading of the pressure P. Pi is the systolic pressure before the medicine is taken and will vary with each patient. However, Pi must fall in the range 200 less than or equal to Pi greater than or equal to 220, for the model to be valid.

a. Determine the rate of change of the systolic pressure P with respect to the amount of drug, x, administered.

b. Determine the minimum amount of the drug that can be administered and still be effective.

c. If a particular patient has an initial systolic pressure of 200 and 10 milligrams of the drug administered, what will the pressure be 30 minutes later?

Note:
For part a. the answer is 2-2x. Is this because Pi is considered a number between 200 and 220 and the equation P=Pi + 2x - x^2 is then used to find the derivative.

• Calculus - ,

a. dP/dx = 2 - 2x
b. In order for dP/dx to be negative (and the drug to therefore be effective, x must be >1 mg.
c. If x = 10 and Pi = 200, then P = Pi + 2x - 2x^2 after 30 minutes
= 200 +20 -200 = 20 mm mercury
Sounds like an overdose to me