HP 15c - Manual (Page 22)

22 Section 1: Using _ Effectively
22
Keystrokes Display
® 029- 34
[ 030- 23
÷ 031- 10
l2 032- 45 2
* 033- 20
|n 034- 43 32
In the previous example, the calculator was set to Radians mode and the three constants were
stored in registers R
0
, R
1
, and R
2
. Key in the same initial estimates as before and execute
_.
Keystrokes Display
|¥
Run mode.
10 ´r 0.1745
60
´r 1.0472 Initial estimates.
´_A 0.4899 Angle given zero slope.
)) 0.0000 Slope at specified angle.
|(|( 0.4899 Restores stack.
vv´B -0.2043 Uses function subroutine to
calculate minimum intensity.
® 0.4899 Recalls θ value.
|d 28.0679 Angle in degrees.
This numerical approximation of the derivative indicates a minimum field intensity of
−0.2043 at an angle of 28.0679°. (This angle differs from the previous solution by 0.0001°.)
Using Repeated Estimation
A third technique is useful when it isn't practical to calculate the derivative. It is a slower
method because it requires the repeated use of the _ key. On the other hand, you
don't have to find a good value for Δ of the previous method. To find a local extreme of the
function f(x), define a new function
g(x) = f(x) − e
where e is a number slightly beyond the estimated extreme value of f(x). If e is properly
chosen, g(x) will approach zero near the extreme of f(x) but will not equal zero. Use _
to analyze g(x) near the extreme. The desired result is Error 8.

If Error 8 is displayed, the number in the X-register is an x value near the extreme.
The number in the Z-register tells roughly how far e is from the extreme value of f(x).
Revise e to bring it closer (but not equal) to the extreme value. Then use _
to
examine the revised g(x) near the x value previously found. Repeat this procedure
until successive x values do not differ significantly.