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 ma
x, justify why. If there is no global minimum, justify why.
1 answer:
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
.
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