If you need symbolic math software and don't have access to Mathematica or Maple, check out maxima (thanks to Aditya for the tip). There are binaries for Windows and Linux, though installing on Mac is a bit more challenging. On Linux, I found xmaxima provided a nice UI if you're not already an Emacs user. --Chloe 12:01, 21 January 2008 (PST)
This will help with 7.42 a If we have a function of n variables, that we want to optimize under a constraint of the form where c is constant, we can use Lagrange multipliers. Basically do
where is the gradient vector of , is the gradient vector of , and λ is a constant to be determined.
You will get n equations of the form , along with the original constraint equation , makes n + 1 equations of n + 1 unknowns, which can be solved to find the optimum (minimum or maximum, to be determined using other means). This method makes 7.42a much, much, much ... simpler.--Nick 17:37, 29 January 2008 (PST)
See Wikipedia for some examples.