Guys I am really stuck with point b of this problem, I am sure somebody can solve it!

Assume that if a ball is placed on an uneven surface it will roll in the direction of steepest descent. That is: it will roll in the direction which maximizes the directional derivative of f where the graph ofz=f(x,y)

describes the shape of the surface.

Suppose we have surface described by the functionf(x,y) = (x^{2}+ 2y^{2})/20

.

- Sketch several level curves for the function and identify their general shape. From your sketches, choose a point and approximate the path of the ball. Where should the ball end up?
- Suppose the ball is at position (
x_{0},y_{0})

at time zero. Find the path the ball will take by setting up and solving a differential equation.- Compute the limit as
t→

of your solution. Does this value agree with your conclusion in the previous exercise?

Thank you very much guys!