https://www.wolframalpha.com/input/?i=local+minima+4x%2B4y+%2C+x%5E2%2By%5E2+%3D+680++%2C+x%3E%3D+3+%2C+y+%3E%3D+3
I'm not familiar with extrema of a function more than 1 variable, but I guess concept of Local/Global max/min will be the same
Clearly, f(x,y) = (18.4391, 18.4391) is not the local minimum ( try x =5 , y = 25.593)
Did Wolfram|Alpha give wrong answer or I'm missing something?
Thanks.