Casio ClassPad II fx-CP400+E User Manual

Chapter 16: Interactive Differential Calculus Application 268
16-1 Learning about Tangents Using the [Tangent] Tab
Consider the slope (differential coefficient) of a tangent to a point on a curve represented by y = f (x).
Two points (D and E) are placed on the graph of
y = f (x), and a straight line (DE) through the two points and the
tangent of point E are drawn. As point D moves infinitely closer to point E, line DE moves infinitely closer to the
tangent of point E. This derives the slope of the line tangent to point E.
u To use the [Tangent] tab
Example: On the graph of y = x
2
− 2, derive the slope of the line tangent to a point (2, 2) on the graph of y =
x
2
− 2.
1. On the application menu, tap
to start the Interactive Differential Calculus application.
2. On the [Function] tab that appears, input
x
2
− 2 into the “y:” line under
“Function”.
3. Tap the [Tangent] tab.
• This will cause the display to appear as shown below.
Point D coordinates (1, −1)
Point E coordinates (2, 2)
y = x
2
− 2 graph (blue)
shows the point that can be moved
using the right and left cursor keys.
Straight line linking point D and point E
(orange)
{Point E y-coordinate} −
{Point D
y-coordinate} (= rise)
{Point E
x-coordinate} −
{Point D
x-coordinate} (= run)
Slope of secant DE (= rise/run)
Expression of secant DE
y = x
2
− 2 tangent to point E (green)
4. Tap w (or Point - Fix Point E).
• This locks point E and allows relocation of point D only.
5. Use the left and right cursor keys to move point D on the
y = x
2
− 2 graph closer and closer to point E.
6. Move point D to the same location as point E.
• This will cause the rise and run values on the [Tangent] tab to become 0, and only the
y = x
2
− 2 (green)
tangent of point E (which is the same as point D) will remain displayed.
• Use the cursor keys to move point D and observe the Slope of secant DE and Eq (equation) of secant DE
immediately before and after the location where point D and point E are identical. This way you can study
the slope and expression of tangent
y = x
2
− 2.
Note
• To switch between the point (D or E) that moves when you press the left or right cursor key, press the up or
down cursor key, or tap 9 or 8. The point that will be moved when you press the left or right cursor key is
indicated by .
• You can also move the point E or point D using the stylus. Tap and hold one of the points with the stylus, and
then drag to the location to which you want to move it.

Casio ClassPad II fx-CP400+E Specifications

General

Model	fx-CP400+E
Category	Graphing Calculator
Display	Color LCD
Resolution	320 x 528 pixels
Color Depth	65536 colors
Backup Battery	CR2032
Connectivity	USB
Power	4 x AAA batteries
Software	ClassPad Manager
Display Size	4.8 inch
Languages	Multiple languages

Summary

Chapter 1: Basics

1-1 General Guide

Provides an overview of the ClassPad, application operations, input, data handling, and format settings.

1-3 Built-in Application Basic Operations

Explains basic information and operations common to all built-in applications.

1-4 Input

Details on using the keypad and the on-screen soft keyboard for data input.

1-7 Configuring Application Format Settings

Configures number format, angle units, and other settings for calculations and graphs.

1-8 When you keep having problems…

Troubleshooting steps for common issues like freezing or unexpected behavior.

Chapter 2: Main Application

2-1 Basic Calculations

Covers arithmetic operations, parentheses, and calculation priority sequences.

2-7 Using the Action Menu

Explains how to use transformation, expansion, and calculus functions via the Action menu.

2-9 Using the Main Application in Combination with Other Applications

Details on using other ClassPad applications with the Main application.

Chapter 3: Graph & Table Application

3-1 Storing Functions

Instructions on how to input and store functions in the Graph Editor window.

3-2 Using the Graph Window

Operations for the Graph window, including display settings, zooming, and panning.

3-3 Using Table & Graph

Covers generating number tables and summary tables from functions.

Chapter 4: Conics Application

4-1 Inputting an Equation

Steps to input conics equations using preset forms or manually.

4-2 Drawing a Conics Graph

Instructions on drawing parabolas, circles, ellipses, hyperbolas, and general conics.

Chapter 5: Differential Equation Graph Application

5-1 Graphing a Differential Equation

Explains how to graph first, second, and nth-order differential equations.

Chapter 6: Sequence Application

6-1 Recursive and Explicit Form of a Sequence

Covers working with explicit and recursive sequences.

Chapter 7: Statistics Application

7-1 Using Stat Editor

Covers creating and maintaining lists for statistical calculations and graphing.

7-3 Performing Basic Statistical Calculations

Details on calculating mean, standard deviation, quartiles, and median.

7-4 Performing Advanced Statistical Calculations

Covers performing tests, confidence intervals, and distribution calculations using wizards.

Chapter 8: Geometry Application

8-1 Drawing Figures

Instructions on drawing basic geometric figures like points, lines, circles, and polygons.

8-2 Editing Figures

Explains how to select, move, copy, and change properties of geometric figures.

8-3 Using the Measurement Box

Details on viewing, specifying, and constraining measurements of figures.

Chapter 9: Numeric Solver Application

Solving an Equation

How to use the Numeric Solver to find approximate solutions to equations.

Chapter 10: eActivity Application

10-1 Creating an eActivity

Basic steps for creating an eActivity, including inserting text, calculations, and data.

Chapter 11: Financial Application

11-1 Financial Application Basic Operations

Covers starting the application, navigating pages, and inputting values.

11-2 Performing Financial Calculations

Details on performing various financial calculations like interest, cash flow, and amortization.

11-3 Calculation Formulas

Provides the formulas used for various financial calculations.

Chapter 12: Program Application

12-1 Creating and Running Program

Step-by-step guide to creating, saving, and running programs.

12-2 Debugging a Program

Techniques for finding and fixing errors in programs.

12-3 User-defined Functions

How to create and use user-defined functions within the ClassPad.

Chapter 13: Spreadsheet Application

13-1 Inputting and Editing Cell Contents

Covers selecting cells, inputting data, formulas, and editing cell contents.

13-2 Graphing

Instructions on creating various types of graphs from spreadsheet data.

Chapter 14: 3D Graph Application

14-1 Inputting an Expression

Details on inputting expressions for 3D graphing using the editor.

14-2 Using the 3D Graph Window

Operations for the 3D Graph window, including view settings and rotation.

Chapter 15: Picture Plot Application

15-1 Using the Plot Function

Covers plotting points on images and overlaying graphs.

Chapter 16: Interactive Differential Calculus Application

16-1 Learning about Tangents Using the [Tangent] Tab

Demonstrates the concept of tangents and slopes using interactive graphs.

16-2 Deriving the Derivative Using the [Deriv] Tab

Explains how to derive and plot function derivatives using the DiffCalc tool.

Chapter 17: Physium Application

17-1 Periodic Table

Accesses and displays information from the built-in periodic table.

17-2 Fundamental Physical Constants

Provides access to fundamental physical constants and their details.

17-3 Precautions

Lists important precautions related to the Physium application's data.

Chapter 18: System Application

18-1 Managing Memory Usage

Information on managing ClassPad memory areas: Main, eActivity, and Storage.

18-2 Configuring System Settings

Guides on adjusting display, power, keyboard, and other system settings.

Chapter 19: Performing Data Communication

19-1 Data Communication Overview

Explains configuring communication parameters and connection modes.

19-2 Performing Data Communication between the ClassPad and a Personal Computer

Steps for transferring data between ClassPad and a computer via USB.

Appendix

Character Code Table

A table listing character codes for 2-byte and other characters.

System Variable Table

An alphabetic listing of system variables with descriptions and types.

Graph Types and Executable Functions

A reference for graph types and functions executable within applications.

Error and Warning Message Tables

Lists and explains various error and warning messages encountered.