Find pt on paraboloid , if it exists, at which the tangent plane is parallel to plane .
Not completely sure how to approach this problem. I'm pretty sure it involves the gradient, so I set and found that gradient which was .
Do I need the equation for the tangent plane of the paraboid? And are -1, 1, 1 the directional numbers for the plane ?
Ok, here's what I've done:
I got confused at this point. I wasn't sure what I do with the x. . There wasn't an x in the equation, and , so does the point exist?
And is there a way to check, if I found a point, that it was a correct point?