Hello

I have been given the following optimization problem:

max 2x+y under x²+y²=20

I used the method of Lagrange multipliers and found that (x,y,)=(4,2,1/4) and (x,y,)=(-4,-2,-1/4)

I have to use the extreme value theorem to explain that there is one solution to the optimization problem. And I have to determine the solution to the problem.

Can someone please help me with this task? The original task is explained in Danish, so I had difficulties translating the terms in English, but I hope it makes sense :-)