@Obliv yes. Lagrange multipliers are just a way to solve for places where the gradient is zero when constrained to a curve. Whether you're at a max or min is unknown.
@rob @heather you both owe a dollar to there pun jar.
@rob I gave an incorrect definition of a tangent plane (not surprisingly since this material is still new to me). It should be $\nabla f(u) \cdot (x-u) = 0$ for some point $u$ and both $g,f$ are normal to $\nabla f$ and $\nabla g$ for this to occur
literally seconds before class I'd scribble random things onto the paper and when he'd come around to check the hw he'd just nod and move on. Sometimes he'd notice and then give me a nice stern look ;P
A manifold is just anything where each little piece can be modeled as an n-dimensional space of real numbers. In other words, it's anything where each little piece can be given a coordinate system involving n coordinates.
