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"Consider the surface given by the equation [tex] x^3 + xy^3 - z^2 = -4 [/tex] The point p = (1,2,3) lies on this surface. Give a vector that is perpendicular to the surface at p?"

I'm not too confident about this question although there is a theorem in my notes saying:

if p exists within the level surface equal to c and the gradient of the function f is not equal to zero, then the gradient at point p is perpendicular to every path in the level surface equal to c which passes through p.

Does this apply here?

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# Homework Help: Perpendicular vector Q

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