When you cough, your windpipe contracts. The speed, v(r), with which you expel air through your...

When you cough, your windpipe contracts. The speed, v(r), with which you expel air through your windpipe, depends in the radius, r, of your windpipe. If a is normal (rest) radius of your windpipe, then for 0<r<a. The speed is given by: v(r)=k(a-r)r^2 where k is a positive constant. For an individual, assume a to be constant. a. Find all critical points of v(r). b. what value of r minimizes the speed? Explain briefly using the second derivative test. c. What value of r maximizes the speed, and what is this maximum speed? explain briefly using the first derivative test. d. Consider two individuals, Jay and Dee. Jay's value of a is larger than Dee's value of a. How would Jay's maximum windpipe velocity compare to that of Dee? Explain briefly.

Expert Solution

part (d) is unclear..

milcah answered 2 years ago

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