I'm trying to find the largest sphere that be inscribed inside the ellipsoid with equation 3x^2 + 2y^2 + z^2 = 6. 2. Relevant equations I know I will need at least 2 equations. One of them is the constraining equation (f(x) = a, where 'a' is a constant) and the other is the equation you want to maximize. I need to use Lagrange multipliers to find a lambda such that (del) F = lambda (del G). 3. The attempt at a solution My first attempt was to maximize the function x^2 + y^2 + z^2 = f(x,y,z) and use the constraining equation for the ellipsoid (3x^2 + 2y^2 + z^2 = 6). However, there is no lambda that will made del (F) = L (del [G]). I think i'm using the wrong equations. Another idea is to find the point(s) on the ellipsoid that lies closest to the origin and use that as the radius for my sphere. However, that boils down to the same equations I already unsuccesfully used. Any help appreciated.