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

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?

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