Discussion
The vector \( \nabla\phi \) at a point of the surface \( \phi = \) constant is
Answer: B
Moving along the surface leaves \( \phi \) unchanged, so the directional derivative in every tangential direction vanishes and the gradient is perpendicular to all of them. That is what makes the gradient the natural way to find a normal, and hence a tangent plane, to a surface given implicitly
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