Question

The slope of the line tangent to the curve defined by the intersection of the elliptic paraboloid z = x ^ 2 + y ^ 2 with the plane x = 1 is given by:

Answer 1

i'm more fabulous :D

Answer 2

Hint:
The paraboloid looks like this:
z=x^2+y^2
A section at x=1 looks like this:

Viewing it on the y-z plane:

At x=1, y=2, z=x^2+y^2=5, thus
(1,2,5) is a point on the surface.

Have you done partial derivatives?