Use Lagrange multipliers to find three positive numbers whose sum is 15 and whose product is as large as possible.
Help please~~
Let be the numbers:
So you will get three conditions from this, . This yields using the fact thay are positive. Substituting in the constaint yields . Thus the maximum value is of product is
(Note that I did not add the constraint that they are positive, and the answer turned out to be positive... so no problem with that)