Answer:
Step-by-step explanation:The rate of change of a function over a specified interval refers to how much the function's output (dependent variable) changes concerning the change in its input (independent variable) over that interval. It is also commonly known as the "slope" of the function.Mathematically, the rate of change (denoted as Δy/Δx) of a function f(x) over the interval [a, b] can be calculated as follows:Rate of Change = (Change in Output) / (Change in Input)
= (f(b) - f(a)) / (b - a)Here, f(a) and f(b) are the function values at the points 'a' and 'b' respectively.Geometrically, the rate of change represents the slope of the line connecting two points on the graph of the function corresponding to the interval [a, b]. If the function is linear, the rate of change is constant over any interval.For non-linear functions, the rate of change can vary across different points of the function's graph, and you might need to calculate it at specific points or use calculus techniques to find the instantaneous rate of change (derivative) at a particular point.