HP 15c Collector's Edition User Manual

Section 13: Finding the Roots of an Equation 189
If you have some knowledge of the behavior of the function f(x) as it
varies with different values of x, you are in a position to specify initial
estimates in the general vicinity of a zero of the function. You can also
avoid the more troublesome ranges of x such as those producing a
relatively constant function value or a minimum of the function’s
magnitude.
Example: Using a rectangular piece of
sheet metal 4 decimeters by 8 decimeters,
an open-top box having a volume of 7.5
cubic decimeters is to be formed. How
should the metal be folded? (A taller box is
preferred to a shorter one.)
Solution: You need to find the height of
the box (that is, the amount to be folded
up along each of the four sides) that gives
the specified volume. If x is the height (or
amount folded up), the length of the box is (8 − 2x) and the width is
(4 − 2x). The volume V is given by
V = (8 − 2x)(4 − 2x)x.
By expanding the expression and then using Horner’s method (page 79),
this equation can be rewritten as
V = 4((x − 6)x + 8)x.
To get V = 7.5, find the values of x for which
f (x) = 4((x − 6)x + 8)x − 7.5 = 0.
The following subroutine calculates f (x):
Keystrokes Display
| ¥
000-
Program mode.
´ b 3
001-42,21, 3
Label.
6
002- 6
Assumes stack
loaded with x.

HP 15c Collector's Edition Specifications

General

Model	HP 15c Collector's Edition
Category	Calculator
Type	Scientific
Power Source	Battery
Manufacturer	HP
Display	LCD
Functions	complex numbers, matrix operations

Summary

Introduction

This Handbook

Outlines the structure of the manual, detailing its parts and how to use it for learning.

The HP Community

Discusses user groups and websites for HP calculator enthusiasts and information sharing.

Part I: HP 15c Fundamentals

Section 1: Getting Started

Covers basic operations like powering on, keyboard layout, and primary/alternate functions.

Section 2: Numeric Functions

Explains essential numeric operations including logs, trig, powers, and conversions.

Section 3: The Automatic Memory Stack, LAST X, and Data Storage

Details the RPN stack, LAST X register, and data storage operations.

Part II: HP 15c Programming

Section 6: Programming Basics

Introduces core programming concepts: creating, loading, running programs, and memory.

Section 8: Program Branching and Controls

Covers controlling program flow using branching, loops, and conditional tests.

Part III: HP 15c Advanced Functions

Section 11: Calculating With Complex Numbers

Covers entering, manipulating, and performing calculations with complex numbers.

Section 12: Calculating With Matrices

Explains matrix operations, including dimensioning, element access, and calculations.

Section 13: Finding the Roots of an Equation

Details using the SOLVE function for numerical root finding and equation solving.

Section 14: Numerical Integration

Explains how to perform numerical integration using the ∫f(x)dx key and subroutines.

Appendix A: Error Conditions

Error 8: No Root

Explains the error when the SOLVE function cannot find a root.

Error 0: Improper Mathematics Operation

Lists and explains errors related to mathematical operations and illegal arguments.

Appendix D: A Detailed Look at SOLVE

How SOLVE Works

Explains the numerical technique and logic behind the SOLVE algorithm.

Finding Several Roots

Discusses methods for finding multiple roots of an equation using the SOLVE function.