Let $\{x_1, x_2, \dots, x_n\}$ be a dataset of real numbers. Consider the function $f(c) = \sum_{i=1}^n |x_i - c|^p$ for $p \ge 1$. For which value of $p$ is the minimizer of $f(c)$ always guaranteed to be the sample median (or one of the medians if $n$ is even)?