Determine whether the following function has a maximum, a minimum, or neither. If it has either a maximum or a minimum, find what that value is and where it occurs. Reduce all fractions to lowest terms.
[tex]f(x)=13 x-2[/tex]
Answer (1)
The function f ( x ) = 13 x − 2 is a linear function.
Linear functions do not have maximum or minimum values.
The slope of the function is positive, indicating it increases without bound.
Therefore, the function has neither a maximum nor a minimum. Neither
Explanation
Analysis of the Function The given function is f ( x ) = 13 x − 2 . This is a linear function. Linear functions do not have a maximum or minimum value because they increase or decrease without bound. The slope of this function is 13, which is positive, indicating that the function increases as x increases. Therefore, it has neither a maximum nor a minimum.
Examples
In economics, a cost function might be modeled as a linear function, where the total cost increases linearly with the number of units produced. Since linear functions don't have a maximum or minimum, it implies that, in this simplified model, there's no limit to how high the cost can go as production increases, and there's no minimum cost besides the fixed costs when production is zero. Understanding this helps in making decisions about production levels and cost management.
