I am doing my test corrections and I have all of them except one.
Find the critical points if the function: f(x,y) = 1/3x^3 + 1/2y^2 + xy+1
So far I have one crit point of (0,0), and I have the both partial derivative but I am not sure what other points there are. The partials that I got are:
f'(x) = x^2 + y
f'(y) = y + x
Am I right so far? If so could somebody help me out there rest of the way? I am not familuar with the math text thing but I am trying to learnn
is it not enough to say the test gives no conclusion? your professor would expect you to find it? we have a degenerate critical point here. you were taught how to deal with those?
if my memory serves me correctly, you can go through the task of factorizing f(x,y) (it is quadratic in y) and finding where it is positive and negative, and use that to determine how the function behaves. if this is for a calc 3 class, i doubt you would be required to go that far though