1. [3 pts] Let z = f(x, y) be the elevation of a hill. What is the direction of steepest ascent at a point x0 = (x0, y0)? State a formula for the rate of change of f in that direction.

2. [3 pts] Write down the two equations used to solve the unconstrained optimization problem: Find the local maxima and minima of the function z = f(x, y), where (x, y) R^2 .

3. [4 pts] Write down the three equations used in the Method of Lagrange Multipliers to solve the constrained optimization problem:

Find the absolute maximum of the function z = f(x, y) on the curve g(x, y) = k.