1. Let's start by understanding the problem: We want to know if a function that has minima must also have maxima. 2. A minimum (plural: minima) of a function is a point where the function value is lower than all nearby points. 3. A maximum (plural: maxima) is a point where the function value is higher than all nearby points. 4. Important rule: A function can have minima without having maxima, and vice versa. It depends on the function's shape and domain. 5. For example, the function $f(x) = x^2$ has a minimum at $x=0$ but no maximum because it goes to infinity as $x$ goes to positive or negative infinity. 6. Conversely, the function $f(x) = -x^2$ has a maximum at $x=0$ but no minimum. 7. Some functions have both minima and maxima, like $f(x) = x^3 - 3x$, which has both a local minimum and a local maximum. 8. Therefore, having a minimum does not guarantee having a maximum. Final answer: A function with minima does not necessarily have maxima.