Hp 50g Calculator: controlling NUMERIC SOLVER search zone

Question

Hi,
I have looked in User Guide about :"Solving equations with one unknown through NUM.SLV" (pages 6-13 and 6-14)
In my opinion , the user guide is wrorng there:
They resresent the number 4.5006E-2 as a solution to this  equation: exp(x)-sin(pi*x/3)=0
x= 4.5006E-2 is NOT a solution for that equation,
x= 4.5006E-2 is an extremum for that function (a local minimum point)
After further reading I understand the Numerical solver will find a ZERO or EXTREMUM,
the same is applied to the command ROOT
(in the case of ROOT command, you cannot know if what was found is a zero or an extremum)
I want to know please How can I narrow (or controll) the search zone of those solvers?
in other HP calculators (like HP42S and HP32SII) you can give TWO start guesses so the search will be ONLY between those two guesses.
Can I do the same here?
Thank you

Answer 1

Hi,
For the form-based solver, a single initial guess close to the desired solution or two guesses between which will be searched can be provided by setting the variable to the value of the guess:
For one initial guess:
First set  X=-3 by entering -3 when X value is highlighted. Highlight the X value again and select SOLVE, the answer of -3.04544...  will be given. (this is explained on p6-15).
For two guesses between which will be searched:
First set  X= {-2 -4} by entering {-2 -4} when X value is highlighted. Highlight the X value again and select SOLVE, the answer of -3.04544...  will be given.
Similarly, the ROOT function can either be provided with a single guess near the desired point, or two guesses between which will be searched.
Format for ROOT with one guess:
3:    exp(X)-sin(pi*X/3)=0      // expression
2:                     'X'      // variable to be solved for
1:                      -3      // initial guess close to the desired point
Executing ROOT will then give the solution of -3.04544...
Format for ROOT with a two-value range for the guess :
3:    exp(X)-sin(pi*X/3)=0      // expression
2:                     'X'      // variable to be solved for
1:                 {-2 -4}      // initial guess range around the desired point
Again, executing ROOT will give the solution of -3.04544...
Note, the manual uses the word "solution" in the context of anything that is either a root, minimum or maximum. (The AUR specifically uses the terms "root or solution" when describing SOLVE, SOLVEVX or ROOT).
Best regards.
Note: I do not work for HP, I just like playing with calculators :-)