# Activities

• • • ##### Subject Area

• Math: Calculus: Applications of the Derivative

• ##### Author 9-12

60 Minutes

• TI-86
• ##### Report an Issue

Recovering a Function from its Derivative: A Graphical Approach

#### Activity Overview

Students use the calculator to visualize a function using the equation describing its derivative and a single point on the function. They start with simple equations and later solve more complex and difficult differential equations.

#### Before the Activity

• Set the calculator to the Differential Equation Graphing mode
• See the attached PDF file for detailed instructions for this activity
• Print pages 1 - 15 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.
Visual Solution:

• Enter the differential equation on the calculator
• Set the initial conditions and the graphing axes
• Graph the solution to the differential equation
• Compare the analytic solution with the graphed solution

• Changing Initial Values:
• Change the initial values and graph the solution
• Observe that the solution corresponding to each set of initial values moves the starting point of the graph

• Entering Several Initial Values:
• Enter several sets of initial values and graph the data
• Observe a shift in the graph

• Slope Fields:
• Use the slope field function to get a general shape of the family of solutions
• A line segment from any initial point that is tangent to the graph is one of the solutions

• Normal Probability Density Functions:
• Enter the differential equation with initial values of y = -1, and x = -3 and the Min and Max values set at -3 and +3
• Set the calculator to connect points every tenth and graph the solution
• Observe the graph is a scaled version of the normal probability density function

• Interactive Specification of Initial Values:
• Graph the slope field associated with the differential equation
• Graph solutions corresponding to specific initial values

• Graphing 2 Equations Simultaneously:
• Enter two differential equations and different initial values
• Select separate style for each graph
• Graph the solutions together
• #### 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