MATH 2210 Final: MATH 2210 Cornell 2210 2010 Fall Final solution Exam
Document Summary
You have 1 hour 30 minutes to complete this exam. You are free to use results from the lectures, but you should clearly state any theorems you use. The exam is printed on both sides of the paper. Good luck! (1) (a) find all the critical points of f (x, y) = x2 6xy + 10y2 and determine their nature. Solution: the gradient f = (2x 6y, 6x + 20y). So the equation f = 0 is equivalent to. This has only one solution (0, 0), therefore (0, 0) is the only critical point. Nd the nature of the critical point, observe that the hessian matrix is. We have det(h) = 2. 20 36 > 0 and trace(h) = 2 + 20 = 22 > 0. Evaluating at (0, 0) gives gx(0, 0) = 0 gxx(0, 0) = 2 gy(0, 0) = 0 gyy(0, 0) = 20 gxy(0, 0) = 6.
