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 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
- 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 (x0,y0)
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!