1. The problem statement, all variables and given/known data Find the points on the level surface xy2z4=1 that are closest to the origin. 2. Relevant equations Lagrange's method for finding extrema 3. The attempt at a solution If I have a level surface F(x,y,z)=c, it's points closest to the origin will be the ones in which the gradient vector points to the origin. A generic vector pointing to/from the origin is G=<x,y,z>, so F must be a scalar multiple of G. I come up with a system of equations ßx=y2z4 ßy=2xyz4 ßz=4x2z3 xy2z4=1. I can first simplify a little bit. ßx=y2z4 ß=2xz4 ß=4x2z2 I can set the 2nd and 3rd equations equal. 2xz4=4x2z2 ----> x= z2/2 I can plug that x into the first 2 equations. (y2z4)/[z2/2]=2[z2/2]z4 ----> y = +/- √(z4/2) Plugging those into the constraint xy2z4=1 ----> z=4(1/10). Am I right? What is the most straight-forward way of solving such a problem?