For the function f(x,y) = 2x^3 + 3xy + 2y^3,
if the values of c and y are constrained to lie on the straight line y+x=1 use the lagrange multiplier method to find the value of (x,y) where f(x,y) has a turning point.
So far I have computed f sub x, f sub y and f sub lambda to produce 3 equations which imply that y=1-x,
6x^2 + 3 -3x + lambda =0 and
6x^2 - 9x + 6 + lamda = 0
at this point I get stuck
My apologies in my post I inputted the wrong equations corresponding to f sub x, etc.
I found the same 3 equations initially and have now found the value of (x,y) by solving the equations simultaneously, I have never seen or used the Lagrange multiplier before however and I do not know what the next steps are?! I have an example I am trying to follow but I cannot see what they have done after they have their (x,y) values.