# Activities

• • • ##### Subject Area

• Math: Calculus: Applications of the Derivative

• ##### Author 9-12

60 Minutes

• TI-86
• ##### Other Materials
This is Activity 2 from the EXPLORATIONS Book:
Differential Equations With The TI-86

## Recovering a Function from its Derivative: A Numerical Approach

#### 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.
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