Hi, i need help in the following question..
Suppose I am on point (3,-8)
i am given F(x,y) = 80 - 2x^2 - y^2,
find the equation of the path i should take (in terms of x and y) if i want to move in the direction of maximum increase of F.
I know that the level curves are ellipses, and was given a hint to solve it by equating v'(u) = gradient vector of F.. where v(u)=(x(u),y(u)) is the vector representing the path.
however im stuck at this point, i wonder if anyone can help me? will very much appreciate it!