key term - 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

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.