The most common way to approach related rates problems is the following:
Identify the known rates of change and the rate of change that is to be found.
Construct an equation relating the quantities whose rates of change are known to the quantity whose rate of change is to be found.
Differentiate both sides of the equation with respect to time (or other rate of change).
Substitute the known rates of change and the known quantities into the equation.
Solve for the wanted rate of change.
Errors in this procedure are often caused by plugging in the known values for the variables before (rather than after) finding the derivative with respect to time. Doing so will yield an incorrect result.
The most common way to approach related rates problems is the following:
- Identify the known rates of change and the rate of change that is to be found.
- Construct an equation relating the quantities whose rates of change are known to the quantity whose rate of change is to be found.
- Differentiate both sides of the equation with respect to time (or other rate of change).
- Substitute the known rates of change and the known quantities into the equation.
- Solve for the wanted rate of change.
Errors in this procedure are often caused by plugging in the known values for the variables before (rather than after) finding the derivative with respect to time. Doing so will yield an incorrect result.