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Day-10-filled - Example 3 Find the relative extrema of the...

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Math 1314 Day 10 Let 2 ) ( ) , ( xy yy xx f f f y x D - = . You will compute ) , ( b a D for each critical point ). , ( b a Here’s the second derivative test for functions of two variables : If D(a, b) > 0 and 0 ) , ( < b a f xx , then f has a relative maximum at ( a, b ). If D(a, b) > 0 and 0 ) , ( b a f xx , then f has a relative minimum at ( a, b ). If D(a, b) < 0, then f has neither a relative maximum nor a relative minimum at ( a, b ) (i.e., it has a saddle point, which is neither a max nor a min). If D(a, b) = 0, then this test is inconclusive.
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Unformatted text preview: Example 3: Find the relative extrema of the function . 2 3 6 6 ) , ( 2 3-+ +-+ = y x xy y x y x f Example 4 : Find the relative extrema of the function 3 2 ( , ) 2 5 f x y x xy y = -+--. Example 5 : An open box with a volume of 48 cubic inches is to be constructed. The box is to have a partition that is parallel to a side of the box, and the amount of material used is to be minimal. What should be the dimensions of the box?...
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