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# 4.4 - 4.4 Modeling and Optimization(Extreme Value Problems...

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Calculus Section 4.4 Page 20 4.4 Modeling and Optimization (Extreme Value Problems) Method for solving extreme value problems Step 1 . Draw an appropriate figure and label the quantities relevant to the problem. Step 2 . Find a formula for the quantity to be maximized or minimized. This is called developing a “mathematical model” for the problem. Step 3. Using the conditions stated in the problem to eliminate variables, express the quantity to be maximized or minimized as a function of one variable. Step 4. Find the interval of possible values for this variable from the physical restrictions in the problem. (This can be done using the graph of the function.) Step 5. Use techniques to obtain the maximum or minimum (use calculus to identify the critical points and endpoints – can always use the graph to verify ) Example 1 Find two numbers whose sum is 20 and whose product is as large as possible. Example 2. Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible.

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