Path of Steepest Ascent.

[descartes75]

Ok I am drawing a blank.
I have a function f(x,y) representing a Temperature field. I am required to plot level curves for different K's and get the Gradient vector from a specific point. I have done all that.
I am also required to PLOT THE PATH of greatest change from the given point and that's where I am stuck.
How can I do that? (other than numerically)

This is a temperature field and I am plotting the path of a heat seeking robot.

The function is 100-x^2-4y^2 but I just need a push in the right direction.

Thanks

 

[arthur ohlsten]

Could you take the derivative, which is the slope of the curve, and then find the greatest slope at the point and follow that path to the next point?
[The slope is in terms of 2 variables.]
I hope this helps
Arthur