How to estimate the instantaneous rate of change?
Understand the Problem
The question is asking about the method to estimate the instantaneous rate of change, which is often related to calculus and specifically the concept of derivatives. The high-level approach would involve identifying the function in question and applying the definition of the derivative or using a limit process, if applicable.
Answer
The derivative at the point of interest.
The instantaneous rate of change of a function at x=a is the limit of the difference quotient (the derivative) evaluated at x=a.
Answer for screen readers
The instantaneous rate of change of a function at x=a is the limit of the difference quotient (the derivative) evaluated at x=a.
More Information
The instantaneous rate of change is essentially the slope of the tangent line to the function's graph at a specific point.
Tips
A common mistake is not making h small enough when estimating, leading to inaccurate results.
Sources
- The web page with info on - University of Texas at Austin - web.ma.utexas.edu
- How do you find the instantaneous rate of change of a function at a point - Socratic - socratic.org
