A question asks me to evaluate the maximum and minimum value of the following function:

$$y=\sqrt{x}+\sqrt{27+x}+\sqrt{13-x}, 0\le x\le13$$

I have tried to compute y using $$x=0,1,2,...,13$$ I believe such maximum occurs at x=9, and the minimum value lies on boundary points, but how can I prove that without calculus?

Thanks!