The following is the mathematical expression for my model's rate expression. Variable $x1,x2$ are the controlling parameter, while the rest are positive constants.
$$\max_{x1,x2} \ x_1\tau_k K\sum_{j=1}^{J}\frac{(-1)^{(j+1)}}{a (j+1)b^{^2}} - \tau_k K + \epsilon c^3x_2^3\ \ (s.t. \ 0<\ x_1 <\ 1,\ 0<\ x_2<\ 1)$$
Can I mathematically say that it is a convex problem within the limits of variables $x1,x2$? The graph for $x^3 \ \forall\ x>0$ strictly follows the definition of convexity.
Furthermore, which mathematical tool can I use to solve this problem? (I will be using Matlab for execution).