Chapter 24, Problem 13P

Video an giography is used to measure blood flow and determine the status of circulatory function. In order to quantify the video an giograms, blood vessel diameter and blood velocity are needed such that total blood flow is determined. Below is the densitometric profile taken from a videoangiogram of a blood vessel. One way to determine consistently where the edge of the blood vessel is from the angiogram is to determine where the first derivative of the profile is an extreme value. Using the data provided, find the boundaries of the blood vessel and estimate the blood vessel diameter. Use both $O\left(h^2\right)\text{ and }O\left(h^4\right)$ centered difference formulas and compare the results.