Guys I am really stuck with point b of this problem... Can anybody help me please?
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 of z=f(x,y)
describes the shape of the surface.

Suppose we have surface described by the function f(x,y) = (x2 + 2y2)/20
.

  1. 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?
  2. Suppose the ball is at position (x0,y0)
    at time zero. Find the path the ball will take by setting up and solving a dierential equation.

the answer to point b should be written as:
- x(t)=
- y(t)=

Thank you very much for your help!