My problem:
Find the maximum value $M$ of the function $$f(x,y) = x^5 y^2 (6-x-y)^7$$ on the region $x\geq0, y\geq 0, x+y \leq 6.$
Solving the system of equations made of the partial derivatives (to find the critical points) is quite lengthy.
Is there another way to go about this?