Education Technology

Recovering a Function from its Derivative: A Numerical Approach

Published on 06/09/2008

Activity Overview

In this activity, students use the calculator to find numerical solution for a function given its derivative and a point on the function.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 17 - 25 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.
    Follow the Activity procedures:
    A Table of Values for a Differential Equation:

  • Enter the differential equation on the calculator
  • Select initial conditions, window viewing parameters, and graphing parameters
  • Graph the solution to the differential equation
  • Use the trace function and trace values of y for different values of x
  • Generate a table of values with all the ordered pairs
  • Compare results in the table (numerical solution) to the values given by the analytic solution

  • Exponential Growth:
  • Enter the differential equation
  • Select initial conditions, window viewing parameters, and graphing parameters
  • Graph the solution to the differential equation
  • Enter the analytic solution and compare it to the graphed solution
  • Generate a table of values for the equation and compare the values to the analytic solution

  • Compound Interest:
  • Formulate a differential equation for the given data of initial investment that increases each year at a definite pace
  • Enter the differential equation
  • To find the amount after 10 years, enter 0 for tMin and 10 for tMax
  • Generate a table of values
  • Use trial and error, to find a closer rate of interest and compare it to the solution of the differential equation
  • Use the table to estimate the amount in 10 years
  • After the Activity

    Students solve problems on the exercise page.
    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary