Difference quotient

Definition

The difference quotient is a formula that provides the average rate of change of a function over an interval. It is commonly used as the basis for defining the derivative.

5 Must Know Facts For Your Next Test

1. The difference quotient formula is $\frac{f(x+h) - f(x)}{h}$.
2. It helps approximate the slope of the secant line between two points on a function.
3. As $h$ approaches 0, the difference quotient approaches the derivative of the function at point $x$.
4. The concept of limits is crucial when working with difference quotients to find derivatives.
5. Understanding how to simplify functions within this formula is essential for calculating derivatives.

Review Questions

• What does the difference quotient formula represent in terms of a function's graph?
• How does taking the limit as $h$ approaches 0 relate to finding a derivative?
• Can you compute the difference quotient for a linear function and explain its significance?

Related terms

Derivative: The derivative represents an instantaneous rate of change and is found using the limit of the difference quotient as $h$ approaches 0.

Limit: A limit describes the value that a function approaches as its input approaches some value.

Secant Line: A secant line intersects two points on a curve and its slope represents an average rate of change over that interval.