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Unformatted text preview: M 427L Each question is worth 10 points, the total is 120 No Graphing Calculators. Put your answers to all the questions on the scantron sheet. Be sure to fill out the top of the scantron sheet. I suggest you look at all of the possible answers before making your choice. You may keep your exam, you need only turn in the scantron sheet. For problems 112 (i.e. the entire exam) let f ( x,y ) : R 2 R be the function f ( x,y ) = x 2 + 4 xy + y 2 . 1. At the point bracketleftbigg 1 1 bracketrightbigg if you move a very small distance in the direction of the vector bracketleftbigg 1 2 bracketrightbigg does f (a) Increase (b) Decrease (c) Stay the same 2. Which of the following is the Hessian matrix for f ? (a) bracketleftbigg 2 4 4 2 bracketrightbigg (b) bracketleftbigg 2 5 4 2 bracketrightbigg (c) bracketleftbigg 2 x 1 y 2 bracketrightbigg (d) bracketleftbigg 2 1 1 2 bracketrightbigg (e) bracketleftbigg 2 8 8 2 bracketrightbigg 3. At the point bracketleftbigg 1 1 bracketrightbigg in the direction of the vector bracketleftbigg 1 2 bracketrightbigg is the graph of f (a) Concave up (b) Concave down (c) Neither 4. (This problem is independent of the others, in particular, it has nothing to do4....
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 Spring '11
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