hey im pretty stuck with this, I've got quite far though, I think..
then df/dx =
Then to find the stationary points, we must equate the differentials to 0, and I get to the 4 points:
(2y, -15), (2y, 8x+15), (-2y, -15), (-2y,8x+15)
Then by using the Hessian matrix
H = fxx fxy
Where fxx = 2x, fyy = 2y - 8x, fyx = -8, fxy = 8y
Then the determinant is
Then you put in the x and y co-ordinates and determine whether is a maxima or minima as < or > 0.
But I don't have any numbers...so if anybody can help or see where I've gone wrong
does NOT mean to solve one equation for x as a function of y (which is what you apparently did to get something like "(2y, -15)".
You can, as Pranas said, solve for x as a function of y: and then put, first, x= 2y into the second equation: which reduces to or . Then, since x= 2y, x= 2(1)= 2 or x= 2(-1)= -2. Two solutions are (2, 1) and (-2, -1). Putting x= -2y into that equation instead, [tex]y^2- 8(-2y)y+ 15= 17y^2+ 15= 0 which has no real solutions.