1. The problem is to show that the function defined by $f(x) = 12$ has no maximum. 2. Note that $f(x) = 12$ is a constant function, meaning it has the same value for every $x$. 3. To examine if the function has a maximum, we must check if there exists a point $x_0$ such that $f(x_0)$ is greater than or equal to all other function values. 4. Since $f(x) = 12$ for all $x$, every function value is equal. 5. A maximum is typically a value strictly greater than others or at least equal but occurs at only one or several points. Here, the function is constant everywhere. 6. Hence, the function does not have a maximum in the usual sense (no unique highest point); it is always 12 everywhere. Final conclusion: Because $f$ is constant, it has neither a maximum nor a minimum in the strict sense, it is constant everywhere with value 12.