Math 105/206 - Quiz 1, Jan 16 2015
IMPORTANT: Write your name AND student number somewhere on this sheet.
No calculators or books. Please write down the procedure that you use (not just the result) to get full marks.
(10 marks total)
Problem 1
(a) Write down a normal vector for the plane represented by the equation 2x − 5y + z = 1 − x − y (2 marks).
(b) Find an equation of the plane parallel to 2x − 5y + z = 1 − x − y and passing through the point (0, 0, 0)
(2 marks).
Problem 2
Given the function f (x, y) = x3 + xy + y 2 :
(a) Compute the partial derivatives fx and fy and find the critical points (2 marks).
(b) Compute the second-order partial derivatives fxx , fyy , fxy , fyx (2 marks).
(c) Use the second derivative test to classify the critical points (2 marks).