Help with Math Homework

[MathStudent17314]

When a foreign object that is lodged in the trachea (windpipe) forces a person to cough, the diaphragm thrusts upward, causing an increase in pressure in the lungs. At the same time, the trachea contracts, causing the expelled air to move faster and increasing the pressure on the foreign object. According to a mathematical model of coughing, the velocity v (in cm/s) of the airstream through an average-sized person's trachea is related to the radius r of the trachea (in cm) by the function

v(r) = 3.5(1 − r)r^2 where 1/2 ≤ r ≤ 1.

Determine the value of r for which v is a maximum. (Round your answers to two decimal places.)

 

[tkhunny]

Can you graph it?
Are you sure you shouldn't be posting in the Calculus section?

 

[HallsofIvy]

Where did you get this problem? I ask because there are a number of different ways to answer this question, of differing difficulty and sophistication, and we do not know which would be appropriate for you.

Graphing the function, as tkhunny suggests, is probably simplest. I would probably differentiate with respect to r and set the derivative equal to 0. That requires that you know Calculus which is why tkhunny mentioned the Calculus section of this board.

 

[Deleted member 4993]

When a foreign object that is lodged in the trachea (windpipe) forces a person to cough, the diaphragm thrusts upward, causing an increase in pressure in the lungs. At the same time, the trachea contracts, causing the expelled air to move faster and increasing the pressure on the foreign object. According to a mathematical model of coughing, the velocity v (in cm/s) of the airstream through an average-sized person's trachea is related to the radius r of the trachea (in cm) by the function

v(r) = 3.5(1 − r)r^2 1/2 ≤ r ≤ 1.

Determine the value of r for which v is a maximum. (Round your answers to two decimal places.)

Instruction to round the answer to two decimal places cries out for calculus. But looking at your previous posts, I think graphing the function would be "expected" route here - similar to your previous HW at:

Please help with my homework

I have completed almost all of the questions but I am stuck on a few and this is one of them. It is due by today so if someone could help it would be greatly appreciated! Local maximum= Local minimum= (smaller x value) Local minimum= (larger x value) Increasing= Decreasing=...

www.freemathhelp.com

If you had shown some work - we would have known more definitely "which way to go" and could we could have provided more definitive guidance.