Final answer:
The minimum of a function is identified by analyzing its behavior to find the lowest value of the function, which can be done graphically or through calculus techniques.
Step-by-step explanation:
When a student asks at what input(s) a function is at a minimum, they are seeking the point where the function's value is the lowest. This often occurs in a mathematical context within economics or calculus. To determine this, we must analyze the function's behavior. A production function, for instance, helps us understand the relationship between inputs and outputs in a process. If we are dealing with a cost function, we want to minimize the costs of input while still producing the desired output. It is also mentioned that a society may reach a non-viable state if the energy return on investment (EROI) is at a 1:1 ratio, as all energy would be used up just in obtaining more energy, leaving none for other societal functions. Therefore, the inputs at which a function is at a minimum can be found by looking at where the marginal cost of producing one more unit is least, which can be illustrated through graphical analysis or calculated using derivatives in calculus.