HP 15c User Manual

Page 21

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Section 1: Using

_ Effectively

21

The accuracy of this approximation depends upon the increment Δ and the nature of the
function. Smaller values of Δ give better approximations to the derivative, but excessively
small values can cause round-off inaccuracy. A value of x at which the slope is zero is
potentially a local extreme of the function.

Example: Solve the previous example without using the equation for the derivative dE/dθ.

Find the angle at which the derivative (determined numerically) of the intensity E is zero.

In Program mode, key in two subroutines: one to estimate the derivative of the intensity and
one to evaluate the intensity function E. In the following subroutine, the slope is calculated
between θ + 0.001 and θ − 0.001 radians (a range equivalent to approximately 0.1°).

Keystrokes

Display

000-

Program mode.

´bA

001-42,21,11

002- 26

003- 16

3

004- 3

Evaluates E at θ + 0.001.

+

005- 40

v

006- 36

GB

007- 32 12

®

008- 34

009- 26

010- 16

3

011- 3

Evaluates E at θ − 0.001.

-

012- 30

v

013- 36

GB

014- 32 12

-

015- 30

2

016- 2

017- 26

018- 16

3

019- 3

÷

020- 10

|n

021- 43 32

´bB

022-42,21,12

Subroutine for E(θ).

\

023- 24

l0

024- 45 0

*

025- 20

\

026- 24

l1

027- 45 1

-

028- 30

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