Questions from Calculus

Q: You are told that there is a function f whose partial derivatives

You are told that there is a function f whose partial derivatives are fx (x, y) = x + 4y and fy (x, y) = 3x - y. Should you believe it?

Q: The paraboloid z = 6 - x - x2 - 2y2 intersects

The paraboloid z = 6 - x - x2 - 2y2 intersects the plane x = 1 in a parabola. Find parametric equations for the tangent line to this parabola at the point (1, 2, -4). Use a computer to graph the parab...

Q: The ellipsoid 4x2 + 2y2 + z2 = 16 intersects the plane

The ellipsoid 4x2 + 2y2 + z2 = 16 intersects the plane y = 2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2).