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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 scan-tron sheet. Be sure to fill out the top of the scan-tron 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 scan-tron 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