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Unformatted text preview: Examples on Optimization Problems (Section 4.7) Example 1 A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area? Guidelines 1. Identify given information and unknowns. Draw a diagram . 2. Form an equation of the unknowns which is to be maximized or minimized . 3. Transform all the unknowns into one unknown (for example x ), using the relationships between them. Then rewrite the equation in Step 2 as the equation of x , for example, Q = f ( x ). 4. Write the domain of the function f . 5. Find the first derivative f of f . 6. Find critical numbers of f by setting f ( x ) = 0. 7. Use the Closed Interval Method or the First Derivative Test? 1 Example 2 A cylindrical can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can....
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 Fall '08
 Noohi
 Calculus, Derivative, Continuous function, Closed Interval Method, Identify given information

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