A quadratic function of two variables is given as
$$ f\left(x_{1}, x_{2}\right)=x_{1}^{2}+2 x_{2}^{2}+3 x_{1}+3 x_{2}+x_{1} x_{2}+1$$
The magnitude of the maximum rate of change of the function at the point $(1,1)$ is__________(Round off to the nearest integer). }