Thread: Maximum and minimum of a function of 2 variables (Lagrange multipliers)

My question is : Can I solve the problem without passing by Lagrange multipliers? Because I have some difficulties by doing so. If not, then I don't want any tip and I'll work harder.
I must find the minimum and the maximum of the function in the ellipse .
So it seems a problem that can be solved via Lagrange multipliers, but I didn't find a way to find , and . (I even had to divide by if but then I found another condition ( if then ...) and even with it I couldn't isolate nor nor ).

The requirement that the two gradients are parallel can also be expressed as



This will produce exactly the same result as using the Lagrange multipliers method (once you've eliminated the multiplier).

Both these methods are a bit impractical here though. Since we're dealing with an ellipse, we can express the main function in terms of one variable.



You will of course also need to find the inner points where

Originally Posted by Spec

The requirement that the two gradients are parallel can also be expressed as



This will produce exactly the same result as using the Lagrange multipliers method (once you've eliminated the multiplier).

Both these methods are a bit impractical here though. Since we're dealing with an ellipse, we can express the main function in terms of one variable.



You will of course also need to find the inner points where

Thank you VERY much. I'll work on that! (I might ask for further help in a few days)