Difference Quotient

In this lesson, we will learn how to find the difference quotient of a given function. The difference quotient is a formula used to find the average rate of change of a function over a specific interval. We are given the formula: [f(x + h) - f(x)] / [h], where f(x) is the function, h is the size of the interval, and x is the point at which the rate of change is being evaluated. This formula lays the foundation for the concept of a derivative in Calculus. As the interval h approaches 0, the difference quotient becomes the definition of the derivative. The derivative represents the instantaneous rate of change of a function at a given point. For these problems, we will basically just be doing a lot of simplifying to get our result. The goal is to cancel h away from the denominator.