Use the function f(x,y) = x²- y²

a) In your discussion for this question, you should focus on first moving along the particular grid lines x=0 in both directions from the origin and then y=0 in both directions from the origin. Make sure you make it VERY clear in what direction you are moving as you discuss ideas. Talk about what the gradient vectors in your vector field indicate. What do they reflect about the surface? Be as specific as possible here. Talk about the direction of the vectors, as well as their lengths. What does it mean about the surface when you see some gradient vectors pointing in towards the origin and others pointing away from the origin?

b) Discuss how you can determine behavior for the function from the contour graph by first moving from the origin along the positive x axis, and then moving from the origin along the positive y axis. Include information about increasing or decreasing and concavity, making sure you explain the "whys".

c) How do cross sections help reinforce what you are saying from the earlier parts? What does this tell you about the surface itself? Be as specific as possible. Again, make it clear what direction you are traveling when you are interpreting your cross section curves.