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
- The difference quotient formula is $\frac{f(x+h) - f(x)}{h}$.
- It helps approximate the slope of the secant line between two points on a function.
- As $h$ approaches 0, the difference quotient approaches the derivative of the function at point $x$.
- The concept of limits is crucial when working with difference quotients to find derivatives.
- 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?
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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.
