Ya I get that, but to use Lagrange Multipliers, I need two sets of equations, and plugging in the 2cost and 3sint into the f(x,y) equation still only leaves me with one equation to use to find a max and min.
That sounds like a good idea, I should have thought of that. But then I am confused as to how to turn the position vector into a function that I can use to find extreme values (min/max).
Homework Statement
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).
Homework Equations
Lagrange Multipliers
Partial derivatives
The Attempt at a...