The concept allows for the determination of the slope of a secant line through two points on a curve. This involves calculating the change in the function’s value divided by the change in the independent variable. As an illustration, consider a function f(x). The expression (f(x + h) – f(x)) / h represents this calculation, where h is a small change in x. Simplification of this expression, often involving algebraic manipulation, yields a more manageable form for analysis.
This process is fundamental to understanding the derivative of a function, a cornerstone of differential calculus. It provides a bridge between the average rate of change over an interval and the instantaneous rate of change at a specific point. Historically, the development of this method was crucial in the advancement of calculus and its applications in various scientific and engineering fields.
