13112an4.8-10

13112an4.8-10 - c Kendra Kilmer February 28, 2012 Section...

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c c Kendra Kilmer February 28, 2012 Section 4.6 - Optimization Problems Strategy for Solving Optimization Problems 1. Introduce variables, look for relationships among these variables, and construct a mathematical model of the form Maximize (or minimize) f ( x ) on the interval I 2. Find the critical values of f ( x ) . 3. Use the procedures developed in previous sections (and below) to find the absolute maximum (or minimum) value of f ( x ) on the interval I and the value(s) of x where this occurs. 4. Use the solution to answer all questions asked in the problem. Second Derivative Test for Absolute Extrema: For a continuous function, f , on any interval, if x = c is the only critical value in the interval where f ( c ) = 0 and f ′′ ( c ) exists, then f ( c ) is an on I if f ′′ ( c ) > 0 an on I if f ′′ ( c ) < 0 Note: The test fails if f ′′ ( c ) = 0. Example 1: Find two positive numbers whose sum is 60 and whose product is a maximum.
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13112an4.8-10 - c Kendra Kilmer February 28, 2012 Section...

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