1. The problem statement, all variables and given/known data The electrostatic potential at each point in the region 4x^2 + 9y^2 <= 36 is given by f(x,y) = 3x^2 + 2xy - y^2 + 5. Find the maximum potentials in the region. (Without using Lagrange Multipliers). The solution also said how to do it with Lagrange Multipliers but I think I understand that but I want to understand how to do it using this method. Also, if someone could tell me what this method is called it would be appreciated. 2. Relevant equations Partial derivatives and parametrization. 3. The attempt at a solution I looked through the full solution and I can see how to do it algebraically but I have some questions/confusions I need to settle.: 1) Why is f(0,0) = 5 not a valid final answer? 2) Why does parameterizing things to use a single variable t help? 3) What's the reasoning behind the 0 <= t < 2π constraint on t? Any input would be GREATLY appreciated! Thanks in advance!