What is a good Multivariable calculus textbook at the university level?

My first observation is that the question is a little unclear. It looks like you calculated the direction of the steepest descent. That's one possible interpretation.

But they could also be asking: - What is the DIRECTION towards the closest point of elevation 0? - What is the shortest path to get to the sea at elevation 0? (integrating length on the curve) In the former case, 3x^2 + 2xy - y^2 = 0 4x^2 - x^2 + 2xy - y^2 = 0 4x^2 - (x-y)^2 = 0 (x-y)^2 = 4x^2 4x = +/- (x-y) y = -3x or y = 5x Now you would either have to integrate length on the curve to determine the shortest path (really hard) or notice that the closest point at sea level is at: (x,y) = (11/26, 55/26) Other than that ... your answer looks correct for the partial derivative, other than the fact that I think you have to take the inverse sign (because you're trying to go DOWNhill).

Good luck!

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.