A study conducted on a patient undergoing cardiac catheterization indicated that the diameter of the aorta was
Question:
A study conducted on a patient undergoing cardiac catheterization indicated that the diameter of the aorta was approximately D millimeters (mm) when the aortic pressure was p (mm of mercury), where D(p) = −0.0009p2 + 0.13p+ 17.81 for 50 ≤ p ≤ 120.
a. Find the average rate of change of the aortic diameter D as p changes from p = 60 to p = 61.
b. Use calculus to find the instantaneous rate of change of diameter D with respect to aortic pressure p when p = 60. Is the pressure increasing or decreasing when p = 60?
c. For what value of p is the instantaneous rate of change of D with respect to p equal to 0? What is the significance of this pressure?
Step by Step Answer:
Calculus For Business, Economics And The Social And Life Sciences
ISBN: 9780073532387
11th Brief Edition
Authors: Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price