They just factored it.
ok just a question about the working out for this problem,
I understand
4x^2 - 8xy - 9y^2 = -637
= 8x - 8y - 8x d/dx(y) - d/dy(9y^2)dy/dx
= 8x - 8y - 8x dy/dx - 18y dy/dx
but where does the + sign come from??? can anyone explicitly show where this comes from.. I think it must come from the product rule but I just cant see it...
(8x-8y)-(8x+18y)dy/dx
NB: I realise what you're trying to say. Nevertheless, the editing (in red) I've done is essential - otherwise what's posted makes no mathematical sense. I can assure you that if this was an answer submitted in an examination or assignment it would lose marks if given in its original form.
A local minimum is a point c such that for all x in an open interval containing c.
A local maximum is a point c such that for all x in an open interval containing c.
Best points to focus on is the critical points, the points where the derivative of the function does not exist or equals 0. Plug these critical points in the original function.