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Unformatted text preview: OPTIMIZATION PROBLEMS The differentiation and its applications can be used to solve practical problems. This may include minimizing costs, maximizing areas, minimizing distances and so on. In solving such practical problems, the biggest obstacle comes from converting the words into mathematical terms. The following is a problem-solving procedure for such problems. 1. Understand the Problem - Often the most important thing is to clearly un- derstand what we have and what we should do. 2. Draw a Diagram - In most problems, it is very useful to visualize the problem. 3. Introduce Notation - Assign a symbol (variable) to the known quantities and unknown quantities. Since we are not studying multi-variable calculus, we can only control one variable at a time. It is often required to eliminate all but one variable by using the relations given in the problem. Also, don’t forget the range of the variable. 4. Formulate the Target - Express the quantity that we want to maximize or minimize in terms of the variable in step 3.minimize in terms of the variable in step 3....
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This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.
- Fall '09