Calculus

5. For the function f(x, y) = y+ 2x2 -1. . Determine the gradient vector at the point (1, -1) for F = y+2x2 -1. . Set f(x, y) =0 to construct the projection of the surface on the xy-plane. This projection on the xy- plane is also known as the level contour (imagine looking at this surface directly from above, you will see its projection). Note that for the level contour, you will only stay in the xy-plane. Determine the equation of the tangent line to this level contour at the same point (1, -1) . Confirm (graphically or analytically) that the gradient vector is indeed perpendicular to this tangent line