1. The problem statement, all variables and given/known data Find the maximum x1, x2, x3, in the ellipsoid x1^2/a^2 + x2^2/b^2 + x3^2/c^2 < 1 and all the places where this value is attained. 2. Relevant equations 3. The attempt at a solution My teacher said to use the lagrange multiplier. So far, I have that we are maximizing x1, x2, and x3 such that x1^2/a^2 + x2^2/b^2 + x3^2/c^2 < 1. In any case, I figured that the constraint would be the equation for the ellipsoid, but I haven't a clue what exactly we would be maximizing for. I would assume the maximum of x1,x2, and x3 would simply be the norm of the vector created by the three values.