Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 12z) k C is the line segment from (3, 0, -3) to (5, 4, 1) (a) Find a function f such that F = Vf. f(x, y, z)= (b) Use part (a) to evaluate Vf. dr along the given curve C.

Consider the function z = 4x²+4y²-4 z = f(x, y). Find equations for the xy-trace, xz-trace, and yz-trace for the graph of Find equations for the level curves f(x, y) = c for c= -3, 0, 1, 4. Then sketch and luoel these curves in the xy-plane (on the same set of axes).