Formulate an application problem that could be modeled mathematically through the graph of the function y=x2+12x+1. Some examples are the cost functions, economy charts, population functions, and modeling an epidemic.

1. For what values of the independent variable does the function have a practical interpretation in the context of your application problem? Explain.
2. In Desmos, draw the graph of the first derivative function and interpret it in the context of your application problem.
3. Find all values, for which the first derivative of the function is and interpret them in the context of your application problem.
4. In Desmos, draw the graph of the second derivative function and interpret it in the context of your application problem.
5. Find all values, for which the second derivative of the function is and interpret them in the context of your application problem