# Global/local optima for this function

I have the following function

$f(x_1,x_2) = \frac{x_1}{x_2+p} + \frac{x_2}{x_1+p}$

where $x_1$ and $x_2$ $\in$ $[0,1]$ and $p > 0$ is a constant

I want to find global/local maxima for this. Please suggest some good methods. I already looked at stochastic ones (like PSO etc) but I am looking for other ways in which I can simplify my function.

• can $p > 0$ ?....... Jul 28 '14 at 6:42
• A necessary condition for f assumes a maximum or local minimum is $\frac{\partial f}{\partial x_1} = \frac{\partial f}{\partial x_2} = 0$. Jul 28 '14 at 6:45
• @8pir yes, i updated the question Jul 28 '14 at 6:46
• Use the second partial test Jul 28 '14 at 12:16

• $\dfrac{\partial f^2}{\partial x_i} = \dfrac{2x_j}{(x_i+p)^3} > 0$ Jul 28 '14 at 10:03