Question

on problem 5 - exam 2 regarding lagrange multipliers, is there a typo or are you expected to infer from the wording that f(x,y,z)=x? If it is not a typo, how do you make this inference? Thanks!

Answer 1

In this case you are asked to find a point on the surface (defined by the constraint g(x,y,z) whose x coordinate is largest. All you are taking into consideration is just this x coordinate, that's why f(x,y,z) = x. Imagine a shape in a 3D space (e.g. a sphere), slice the space with vertical planes with equation x = x0. Now vary x0. The highest value of x0 that you can get while still slicing at least one point of the shape is the searched value of f(x,y,z) = x.