I am having trouble trying to follow a textbook example of such a problem. Using the Lagrange's Multiplier method, we could set up a set of equations like below:
$g(x,y,z)=x^2+y^2+z^2-1=0, x>0, y>0, z>0$
then the lambda could be found by solving
suddenly, the textbook jumps right to the conclusion that
How is it derived exactly? I've tried googling and searching for answers but I had no luck finding anything. If someone could break it down step by step, it'd be greatly appreciated. Thanks.