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.

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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

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