1. The problem statement, all variables and given/known data Determine the highest and lowest elevations given by the height z = f(x,y) = 1 - (1/16)x^2 - (1/9)y^2 on the path r(t) = <2cos(t), 3sin(t)>. The xy position on the path at time t is given by r(t). 2. Relevant equations Lagrange Multipliers Partial derivatives 3. The attempt at a solution I was going to try using the Lagrange Multiplier method to find the extreme values of the function f(x,y), but I would need the xy position to be given as an equation and in x and y terms. I am confused as to how to do this because we are given a position vector instead, in terms of t. Could anyone help me out and guide me with how to do this?