Math 208 (Lutz) - Quiz #6, 10/11/13
Name:
Directions: This quiz has 3 questions, for a total of 20 points. Solve each problem carefully. You must
show ALL of your work in order to earn full credit.
1. (8 points) For the function f (x, y) = −3
x2 + 6xy − 3y + 1, find the critical points and classify them
2
as local maxima, local minima, saddle points, or none of these.
2. (5 points) Let R be the region 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. Dividing R into 4 equal squares, use Riemann
sums to make an upper estimate on the volume of the region above R and under f (x, y) = 2x2 + 1.
3. (7 points) Use Lagrange multiplies to find the maximum and minimum values of f (x, y) = x + 3y + 2
subject to the constraint x2 + y 2 = 20.