Final answer:
The student must find the value of x where the marginal cost is the same as at x = 0. This involves solving an equation with the marginal cost function, but a numerical answer cannot be provided without the specific function. Understanding economic implications like the zero profit and shutdown points is also crucial.
Step-by-step explanation:
The student is tasked with determining the value of x at which the marginal cost (C'(x)) returns to C'(0). Given that marginal cost represents the change in total cost when an additional unit of output is produced, the question requires knowledge of calculus to find the value of x that equates a given marginal cost function back to its initial value at x = 0.
To solve this, we would need the actual marginal cost function, and then we'd set C'(x) equal to C'(0) to find the corresponding value of x. However, without the explicit function provided, we can't give a numerical answer. It is also important to understand economic implications in such a scenario, such as the zero profit point and the shutdown point, to provide a comprehensive explanation.