How do I solve this problem:

When a foreign object lodged in the trachae(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) of the airstream through an average size person trachae is related to the radius (r) of the trachae ( in centimeters) by the function: v(r)=3.2(1-r)r^2, wher 0.5<r<1. Determine the value of R for which V is a maximum.

To find a mximum (or a minimum)of te hfunction v(r), find the value of r for which dv/dr = 0. Then to see whether the value you get is a max or a min, find the value of the second derivative at this point r - if the 2nd derivative is negative at that point you have a local maximum, and if the 2nd derivative is positive, you have a local minimum. Post back and tell us what you get for r.