# Calculus III differentiation problem

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• Mar 20th 2013, 02:01 PM
MatteoManfredi
Calculus III differentiation problem
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
.

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 differential equation.
3. Compute the limit as t http://www.webassign.net/images/infinity.gif
of your solution. Does this value agree with your conclusion in the previous exercise?

Thank you very much guys!
• Mar 20th 2013, 02:27 PM
HallsofIvy
Re: Calculus III differentiation problem
What have you done and where are you stuck? The first problem asks you to "Sketch several level curves for the function and identify their general shape". Have you done that? Do you know what "level curves" are?
Do you know what the "directional derivative" of f is?
• Mar 20th 2013, 02:51 PM
MatteoManfredi
Re: Calculus III differentiation problem
Yes, I know what they are and I know what a directional derivative is. My problem is that I have to express both x and y as a function of t and I really do not know how to do. The answer should be something like x(t)=.... and y(t)=...