Hi, I have a strangely worded problem that I'm having problems interpreting/solving
(calculator active) The rate of change R, in km/hr, of the altitude of a hot air balloon is given by for time 0<(or equal to) t <(or equal to) 4, where t is measured in hours. Assume the balloon is initially at ground level.
a. what is the max altitude of the balloon during the interval given above?
Well, since the equation given above is the rate of change I plugged it into my calculator to find the critical points, I got t=1.572 and t=3.514. I then took the derivative of that equation and plugged in my critical points to determine the max. I got a max from t=1.572
I know there is a max altitude at time = 1.572 but how do I figure out what the altitude is at this time? I know I have to come up with a position equation but I'm a little lost on that.
All help is appreciated, thanks.