Math 208 (Lutz) - Quiz #4, 9/20/13
Name:
Directions: This quiz has 3 questions, for a total of 18 points. Solve each problem carefully. You must
show ALL of your work in order to earn full credit.
1. (5 points) The price P in dollars to purchase a used car is a function of its original cost, C, in dollars,
and its age, A, in years. Answer the following two questions about this function.
(a) What are the units of ∂P/∂A?
(b) What is the sign of ∂P/∂A, and why?
2. (5 points) Consider the function f (x, y) = x ln(y cos x). Calculate the partial derivative
!
∂f !!
.
∂y !(π/3,1)
3. (8 points) Give the local linearization of g(x, y) = e−x sin y at (1, 2). Use it to estimate g(0.9, 2.2).
Compare this estimate to the actual value of g(0.9, 2.2).