What is the definition of a derivative?
Understand the Problem
The question is asking for the definition of a derivative, which is a fundamental concept in calculus related to the rate at which a function is changing at any given point.
Answer
The derivative is the limit of the change in the function as interval approaches zero, indicating the slope of the tangent line at a point.
The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero, and is often interpreted as the slope of the tangent line at a particular point.
Answer for screen readers
The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero, and is often interpreted as the slope of the tangent line at a particular point.
More Information
The concept of a derivative is crucial in calculus as it allows for understanding how a function changes at any given point, often applied in physics and engineering to represent rates such as speed or acceleration.
Tips
A common mistake is confusing the derivative with the function itself rather than understanding it as the function's rate of change.
Sources
- Calculus I - The Definition of the Derivative - Pauls Online Math Notes - tutorial.math.lamar.edu
- Derivative | Definition & Facts - Britannica - britannica.com
- Derivatives - Calculus, Meaning, Interpretation - Cuemath - cuemath.com
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