- #1

s3a

- 818

- 8

## Homework Statement

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.

## Homework Equations

Partial derivatives and parametrization.

## 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!