When a person coughs, his or her trachea (windpipe) contracts, allowing air to b

Question

When a person coughs, his or her trachea (windpipe) contracts, allowing air to be expelled at a maximum velocity. It can be shown that during a cough the velocity v of the airflow is given by the function v = f(r) = kr2(R ? r), where r is the trachea's radius during a cough, R is the trachea's normal radius (both measured in centimeters), and k is a positive constant. Find the radius r for which the velocity of the airflow is the greatest (that is, find the absolute maximum value of v on the interval [0, R]). Your answer will be in terms of R

Explanation / Answer

v=kr^2R-kr^2r, where k, R are constants dv/dr=2kRr-3kr^2 finding the maxima by equaling to zero 0=2kRr-3kr^2

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.