Hi.

I attempted to solve this problem by first finding the partial derivatives of z with respect to x and y. Then I attempted to find the equation of z when x = 4 (since it is the plane). I found the velocity vector and took the derivative of that, then pugged that into the equation for r, using the point as the initial values, but that's wrong. I'm not really sure what I'm doing wrong. I may be visualizing the problem incorrectly. I would really appreciate if someone could help walk me through this problem.

Thank you.

The paraboloid z = 8 - x - x2 - 3y intersects the plane x = 4 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (4, 2, -24). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.) x(t) = 4, y(t) = 2+ t, z(t) = -6t-24 X