Estimating derivatives using data

Estimating derivatives using data

Author: Keely Baker

The student will study a table of data from a function and determine the approximate rate of change at a point.

Using the information given in a table, we can estimate the instantaneous rate of change at a point by using the slope formula learned in Algebra.  This is because the slope of a function is the average rate of change and at some point on a continuous interval, the average rate of change is equal to the instantaneous rate of change.

See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to over 2,000 colleges and universities.*

Begin Free Trial
No credit card required

27 Sophia partners guarantee credit transfer.

245 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 21 of Sophia’s online courses. More than 2,000 colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.


Average rate of change versus Instantaneous rate of change

This video shows how to find average rates of change.

Source: Sanfordflipmath AP Calculus

Finding derivatives using data from a table

Full Screen

Source: Nancy Stephenson, AP Calculus Conference, SMU at Plano, TX