$f\left(x_1,x_2\right)=x_1^3+3x_2^3-9x_1x_2$
Find the maximum given that $x_1,x_2≥1$
Just some added info: I know that I have to find the first order and second order partial derivatives; however when I try to find the critical points for $x_1$ or $x_2$ I always get weird numbers. Any help appreciated.
Hint: $f(t,t) = 4t^3 - 9t^2.$ Does $4t^3 - 9t^2$ have a finite maximum on $[1,\infty)?$