Use Lagrange multiplier techniques to find the local extreme values of the given function subject to the stated constraint. If appropriate, determine if the extrema are global. (If a local or global extreme value does not exist enter DNE.)f(x,y) = 5x + y +2 with constraint g(x,y) = xy = 1

You haven't told me what the question is.  But I put the mouse
to my forehead, closed my eyes, took a deep breath, and I could
see it shimmering in my mind's eye.  It was quite fuzzy, but I think
the question is

                   "What score does Andrew need on the next test
                     in order to raise his average to 72% ?"

The whole experience drew an incredible amount of energy
out of me, and the mouse is a total wreck.  So we'll just go ahead
and answer that one.  I hope it's the correct question.

The average score on 4 tests is

                                     (1/4) (the sum of all the scores) .

In order for Andrew to have a 72% average on 4 tests,
the sum of the 4 scores must be

                                         (4) x (72%)  =  288% .

Out of that total that he needs, he already has 

                            (64% + 69% + 73%) = 206%

on the first three tests.

So in order to average 72% for all 4 tests,
he'll need to score

                             (288%  -  206%)  =   82%

on the fourth one.