1. The problem statement, all variables and given/known data Consider the surface and point given below:- Surface: f(x,y)= 4-x2-2y2 Point: P(1,1,1) a) Find the gradient of f. b) Let C' be the path of steepest descent on the surface beginning at P and let C be the projection of C' on the xy-plane. Find an equation of C in the xy-plane. 2. Relevant equations 1) ∇f = <fx , fy> 2) 3) 3. The attempt at a solution a) ∇f = <fx , fy> = <-2x, -4y> b)Descent means -∇f = <2x,4y> Subbing in P(1,1,1) -∇f = <2,4> ⇔ <1,2> Unit vector for descent, u = (1/√5) <1,2> ,where <1,2> is the direction vector of the descent gradient. I am really stuck here. I am not sure what they mean by the projection on the xy-plane. So are we moving from xyz to xy dimensions? And can I am not sure if I should use the projection formulas in this case or use derivatives to get the projection. Please help!!