In summary, related rates involve working with two equations to find the relationship between two quantities and their derivatives. A typical problem would give an equation for angle of elevation and horizontal distance, and you would solve for the derivative of the angle of elevation at a given time. There are resources available online, such as the one provided, for further understanding of this concept.
I am reading about related rates in my calc book but it doesn't really explain it very well. Are there any arcitcals some one can send me that goes indepth about this concept on related rates?
Thank you.
The concept itself isn't that big a deal, so I don't believe there's really much to discuss in depth about it. In these kinds of problems you will be working with two equations. The first equation gives a relationshipw between two quantities in the problem. The second equation gives a relationship between the derivatives (i.e., rates of change) of the first two quantities.
A typical problem goes something like this:
A plane is flying at a constant speed of 120 mph at a constant altitude of 10,000 ft away from an observer on the ground. At what rate is the observer's angle of elevation to the plane changing three minutes after the plane flies directly over the observer?
The first equation I referred to would be an equation that relates the angle of elevation ([itex]\theta[/itex]) and the horizontal distance (x) the plane has flown at an arbitrary time. The second equation (the related rates) would involve d[itex]\theta[/itex]/dt and dx/dt. You would solve for d[itex]\theta[/itex]/dt, and evaluate it at the indicated time.