Got this problem on a test wrong, I misread it quite badly.
According to one model of coughing, the flow F (volume per unit time) of air through the windpipe during a cough is a function of the radius r of the windpipe, given by:
for , where k is a constant and r0 is the normal (non-coughing) radius.
a) Find the value of r that maximizes the flow F.
b) According to the same model, the velocity v of air through the windpipe during a cough is given by:
for . Find the value of r that maximizes the velocity v.
c) During a cough, the windpipe is constricted. According to parts (a) & (b), is that likely to assist or hinder the cough?
Lengthy problem. On my test I differentiated incorrectly, and that messed up my whole problem. How do I do this right?