What mathematical concept is used to calculate instantaneous rates of change of a function?

The concept used to calculate instantaneous rates of change of a function is differentiation. Differentiation is a fundamental process in calculus that allows us to find the derivative of a function. The derivative represents the rate at which the function's value changes at any given point, effectively measuring how steep the curve of the function is at that specific point.

This is particularly important in various applications, such as physics, where it can describe the velocity of an object at a specific moment in time or the rate of growth in economics. The process involves taking a limit as the interval approaches zero, allowing us to ascertain the instantaneous rate of change rather than an average over an interval.

In contrast, integration deals with accumulation of quantities, such as area under a curve, whereas summation involves adding discrete values and correlation refers to the relationship between two variables. Therefore, differentiation is the correct choice for calculating instantaneous rates of change.