Math 208 (Lutz) - Quiz #4, 2/14/14
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. Consider the surface S given by the equation x2 + y 2 − xyz = 7.
(a) (3 points) Give a function g(x, y, z) so that for some constant c, the graph of the given surface S
is the level surface g(x, y, z) = c.
(b) (4 points) Using the function g(x, y, z) from above, give an equation for the tangent plane to the
surface S at the point (2, 3, 1).
2. (6 points) Compute all four second-order partial derivatives of f (x, y) = sin(x/y). Verify that fxy =
fyx .
3. (7 points) Suppose z = f (x, y) = cos(x + 4y), where x = 5t4 and y = 1/t. Let z = g(t). Compute
g ! (t) using the chain rule. Express your answer as a function of t.