Question

Find the maximum and minimum values of the function f(x,y) = xy subject to the constraint x2/2 + y2/2 = 1. Give the maximum and minimum values and the points at which they are attained.

Answer 1

make use of lagrange multiplies.

Answer 2

I tried it but was not able to do it...

Answer 3

or you can express y in terms of x from that constraint ... use that to substitute y in the function that you were to minimize. which makes your function single variable.

but it's better to make use of lagrange multiplies.

Answer 4

are these the one you want to optimize?