Hey I got a question on the Lagrange Multiplier. Let's say the constraint is x+y=3 and the function is f(x,y) = 3x^2+y^2. Now if we think about this geometrically, there will just be a line diagonal line on the surface of f. Therefore, no gradient vector of f will have the same direction as the gradient vector of x+y=3. Does that mean there is no maximum or minimum? Does this also mean that the constraint has to be a closed function? (Like a circle or something instead of a line)?