HP 15c User Manual
Page 21
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