Role of a modelling error an optimization problem

Suppose that the response function f depends on a parameter x as shown at the right, and that x usually varies in the interval [A, B] 
To model this process, we normally use the linearized model: 
f 1 = a x   with the adequate results.
We maximize the response f 1(x), where  x as a control. The optimization pushes x out of its original range. The linear model predicts the unlimited increase of x and of the response  f 1(x).
It would be a mistake to keep the linear model, artificially restricting the range of parameter (forbidding x to exceed an unjustified value C). The result f_c would be far from the real optimum f_opt
Instead, one should improve the model. 


All errors in the model are magnified by the optimization.