Calculus word problem.

[nothingelse]

I'm so lost with this word problem. I know it has to do with difference (dV/dt) but I have no clue where to start or how to finish.
Here it goes..

When hyperventilating, a person breathes in and out extremely rapidly. A spirogram is a machine that draws a graph of the volume of air in a person's lungs as a fuction of time. During hyperventilation, the spirogram trace might be represented by V= 3 - 0.05cos(200pi) where V is the volume of the lungs in liters and t is the time in minutes
a) what are the maximum and minimum volumes of air in the lungs?
b) what is the period of this function?
c) sketch the graph of one period of this function, starting at t=0.
d) find the maximum rate (in liters/mins) of the flow during inspiration. This is called peak inspiration flow
e) find the average rate of flow during inspiration. This is callled the mean inspiratory flow

Help pleasE??

 

[stapel]

a) To find the max/min values, differentiate. The derivative will be a trig equation in sine, whose max/min values will be the amplitude. (Note: There is a typo in your equation, but I don't know where the variable belongs, or what else may have been omitted, so I cannot be specific about the result you're likely to get.)

b) Apply what you learned back in your trig class.

c) This is just trig.

d) If I understand this correctly, it is asking for the maximum value of dV/dt. So differentiate again, set the result equal to zero, and solve. Then plug the critical point(s) into dV/dt, and find the max value.

e) The average value of f(x) over an interval [a, b] is given by the integral of f(x) over the interval, divided by the interval length. I think that's what this part is asking for.

Eliz.