Lagrange Multiplier Fanatics

Question

Given f(x,y)=e^-xy subject to the constraint x^3+y^3=16

the max and min points im getting are both e^4. Is this totally incorrect?

Answer 1

You would not be asking the question if your answer made sense. If a max and min are the same, the function is constant. Also, you forgot a negative sign. e^-4 is the minimum value of the function when x = 2 and y = 2: the maximum value of xy when x^3 + y^3 = 16 is 4

Note that as x goes to positive infinity or negative infinity, y approaches negative infinity and positive infinity, respectively, so -xy goes to infinity and e^-xy goes to infinity. Thus, there is no maximum. There being no maximum does not mean that e^-4 is the maximum.