Guidelines for Solving Applied Minimum and Maximum Problems
- Identify all given quantities and all quantities to be determined. If possible, make a sketch.
- Write a primary equation for the quantity that is to be maximized or minimized.
- Reduce the primary equation to one having a single independent variable. This may involve the use of secondary equations relating the independent variables of the primary equation.
- Determine the feasible domain of the primary equation. That is, determine the values for which the stated problem makes sense.
- Determine the desired maximum or minimum value by applying techniques like the First and Second Derivative Tests.