Don't forget your constraint: so that . Putting that into gives . Of course, that is a polynomial of degree a- 1 or b-1, whichever is larger, and there is no simple way of solving that.
Use the method of lagrange multipliers to determine the maximum value of f(x,y)= x^a y^b (a and b are two fixed positive constants) subject to constraint x + y= 1. (assume x,y bigger than zero)
Help would be appreciated! I get ax^a-1 = bY^b-1 but dont know how to do the rest. I cant isolate x based on only a and b.