Related Rates (Implicit Differentiation Word Problems)

Related rates problems are word problems that require you to apply implicit differentiation as a part of your solution process. These types of word problems traditionally ask you questions about how quickly, fast, or slow something is occurring (growing, shrinking), in other words, its rate of change. They will usually just want to know the rate at which some piece of the problem is changing at a specific moment in time.

Related rates problems are doing just that, they are providing you several different rates of change that are all related through a common equation. For example, the volume of a cylinder equation, , is an equation that relates the volume, the height, and the radius. You would be able to consider how the rates of change of all those variables are related. Remember math people are not creative namers.

Keep in mind that this style of problem is only asking you about how something is changing (shrinking, growing), its rate of change. Related Rates problems are not going to be asking you to find the max or min of an equation.