Lecture4.7Examples.pdf - Calculus Section 4.7 Optimization Problems Examples from Lecture Page 1 of 3 1101 Calculus I 4.7 Optimization Problems \u2022 The

Lecture4.7Examples.pdf - Calculus Section 4.7 Optimization...

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Calculus Section 4.7 Optimization Problems: Examples from Lecture Page 1 of 3 1101 Calculus I 4.7 Optimization Problems The Method of Solution: 1. Understand the problem. 2. Draw a diagram. 3. Introduce notation ( Q is to be maximized or minimized) 4. Find relation between quantities ( Q and all others) 5. Make the relation look like Q = f ( x ) (one variable) 6. Solve f ( x ) = 0 for x . 7. Explain whether you have found a max or min, and if possible if it is an absolute extrema (Closed Interval Method, First Derivative Test, Second Derivative Test, argue based on the geometry of the problem) 8. Write a concluding statement. Example A farmer has 2400 ft of fencing. What are the dimensions of the rectangular pen that produce the largest area? Understand the problem: We need a rectangle. The rectangle should have maximum area for a given perimeter. Draw a diagram : x A y Introduce notation and find relations: The perimeter is P = 2 x + 2 y . The area is A = xy . This is what we want to maximize.
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  • Fall '11
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  • Derivative, Mathematical analysis

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