Solving Optimization Problems Involving Polynomial

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Blendeman - 2C

2.4 solve optimization problems involving polynomial, simple rational, and exponential functions drawn from a variety of applications, including those arising from real-world situations.
2.5 solve problems arising from real-world applications by applying a mathematical model and the concepts and procedures associated with the derivative to determine mathematical results, and interpret and communicate the results.

For these expectations students need to take their prior knowledge of derivatives and apply that knowledge to real world application problems. Students may be faced with a problem and then have to decode what that problem is asking them to do. From the information that they are given they would have to create and apply a mathematical model that will allow them to solve the problem.

Example: A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fencing along the river. What are the dimensions of the field that has the largest area?

This example gives students an idea of how the concepts that they are learning in the course can be applied to real world situations. The problem does not provide the students with the needed mathematical model, but gives them all the needed information to create a model that will help them solve the problems. Students have to recognize that this is an optimization question dealing with maximizing an area.

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