Suppose that I have the following model
$$g(\mu)=\beta_0+\beta_1(x_1-\bar{x}_1)+\beta_2(x_2-\bar{x}_2)+\beta_3(x_2-\bar{x}_2)^2$$
where $g(\mu)$ is the complementary log-log function.

I calculated the increments in the mean for each unit change in the values of $x_1$ and $x_2$ fixing a value of $x_1$ then fixing the values of $x_2$.

Fixing the value of $x_2$ I can calculate the increment in $g(\mu)$ as

$$g(\mu_1)=\beta_0+\beta_1((x_1+1)-\bar{x}_1)+\beta_2(x_2-\bar{x}_2)+\beta_3(x_2-\bar{x}_2)^2$$
$$=g(\mu)+\beta_1$$

Fixing now the value of $x_1$ then

$$g(\mu_2)=\beta_0+\beta_1(x_1-\bar{x}_1)+\beta_2((x_2+1)-\bar{x}_2)+\beta_3((x_2+1)-\bar{x}_2)^2$$
$$=g(\mu)+\beta_3+2\beta_3(x_2-\bar{x}_2)$$

So these are the increments in the values of $g(\mu)$ to calculate the increments in $\mu$ I just calculate the inverse of link function?

How I can find a interval estimation (Bayesian) for those increments too?