Partial Derivatives:

Find the slope of the tangent to the curve of intersection of the surface 36z = 4x^2 + 9y^2 and the plane x = 3 at the point (3, 2, 2).

Question

Partial Derivatives:

Find the slope of the tangent to the curve of intersection of the surface 36z = 4x^2 + 9y^2 and the plane x = 3 at the point (3, 2, 2).

anonymous · Answer

Does x=3 define a plane? I believe it does not.

anonymous · Answer

Oh, wait. That line, plus the point (3,2,2) does. Nevermind.

anonymous · Answer

If you are intersecting the plane x=3 to get the curve, the tangent line will lie on the plane.  So the slope of the line with respect to x is 0.  So I'm guessing they are looking for the slope dz/dy.

So since we are on the plane x=3, replace x with 3 in your equation.  Now you have z as a function of y.  Solve for dz/dy.  Plug in the point (x=3,y=2,z=2).