Education Technology

First Principles

Activity Overview

Students use the two function definition tools on the TI-30XPlus MathPrint calculator to neatly define the function f(x) and then g(x) for the gradient function using differentiation from first principles. By repeatedly decreasing the distance between the two points (limit) students can see the gradient also approaches a limit. This tool is then used to generate a list of gradient estimates with a view to establishing the rule for the gradient.

This activity includes a video tutorial.


Students use function notation to express the gradient from first principles for a range of functions to explore the gradient at a point, followed by the general gradient of the function by generating a table of values. 


  • First Principles
  • Gradient
  • Limit
  • Function

About the Lesson

Students define their function f(x) using the function editor on the calculator. The derivative from first principles is then expressed, using a vinculum in appropriate function notation and the distance (d) between the two points is reduced so students can explore the limit. With a small value of (d), students can then store the expression as g(x) and generate a table of values to see the derivative at multiple points with a view to determining the equation for the derivative.

Watch the activity tutorial