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Unformatted text preview: B.2) (After Sept. 24, 12 pts.) Let f ( x, y ) := x 2 + 6 xy + 9 y 2 + 5 (a) What are the critical points of f ( x, y )? (b) What does the second derivative test say about their type? (c) What is their type? (d) Describe the shape of the graph. B.3) (After Oct. 1) Suppose that two intersecting lines are both level curves for a dierentiable function f ( x, y ). (a) (12 pts.) Prove that the point where the two lines intersect must be a critical point. (b) (8 pts.) Must it be a saddle point? (If YES, explain why; if NO, give a counterexample.) Reminder: Please write Sources consulted: none at the top of your homework, or list your (animate and inanimate) sources. See the course information sheet for details. 1...
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This note was uploaded on 09/14/2011 for the course MATH 18.02 taught by Professor Auroux during the Fall '08 term at MIT.
 Fall '08
 Auroux
 Multivariable Calculus

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