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) = (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 dierential equation.
the answer to point b should be written as:
- x(t)=
- y(t)=
Thank you very much for your help!