The Fellowship of the Ring traveling through the mountains ofMoria (which are described by the functionf(x,y)=12x2y2e(-x2-y2))and they find themselves at the point A=(1.5, -1, 1.05). They needto get to the top of the mountain they are climbing so they decideto travel along the plane y=-1. How steep is their climb when theystart at point A? A diagram:https://www.geogebra.org/3d/jbkkyugx
What if they decided to go in a different direction, say theystarted walking towards the point (0,0,0) on a plane that is“verticalâ€. How steep would be the mountain going in thatdirection?
What is the general equation for planes that are vertical, likethe one that you used to travel from A to (0,0,0)?
What would change in your calculations if we change where pointA is? Can you generalize how to find the steepness in differentdirections from a given point A?
