1. Find expressions for all first and second order partial derivatives of the following functions.

a. =$+2+ b. = ( + )

PARTIAL DIFFERENTIATION

)* (

2. Use the small increments formula to estimate the change in

   = $+ - + 4

   when

   1. x increases from 1 to 1.1, and y remains fixed at 0

   2. x remains fixed at 1, and y decreases from 0 to -0.5

3. Use implicit differentiation to find dy/dx.

   $ 2/ = 3

   What is the value of the derivative at x=1, y= -1?

4. A firms profit function for the production of two goods is given by

   = 243 3$ 3$ $$ + 33$ 43

Find the output levels need to maximize profit. Use second-order derivatives to confirm that the stationary point is a maximum.