The symbol "∇f" represents the gradient of a function f. The gradient is a vector that points in the direction of the steepest increase of the function. It tells us how the function changes as we move in different directions. For example, if f represents the height of a hill, then "∇f" indicates the direction you should walk to climb the hill most quickly. In mathematical terms, the gradient is calculated using partial derivatives, which measure how f changes with respect to each variable. This means "∇f" provides valuable information about the function's behavior, helping us understand its maximum and minimum points in various fields, such as physics and engineering.