Find the global maximum and global minimum values (if they exist) of x 2 + y 2 in the region x + y = 1. If there is no global max, justify why. If there is no global minimum, justify why.

Given that , we have , so that

Take the derivative and find the critical points of :

Take the second derivative and evaluate it at the critical point:

Since is positive for all , the critical point is a minimum.

At the critical point, we get the minimum value .

step-by-step explanation: