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 diﬀerentiable 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...
View
Full Document
 Fall '08
 Auroux
 Derivative, Multivariable Calculus, saddle point, Graph of a function, Stationary point, hessian matrix

Click to edit the document details