nSolve error on nSpire CX

[Hartman, B]

OK... I was showing my Precalc class how to check a rational equation with nSolve.  I warned them that it will only give one answer.  I then showed how to tell it where to start, so I had them enter ",2" and found no more solutions.  Since the one and only answer was at -0.5, we did that and it showed -0.5 as a solution.  I then had them do -.499 to start, and it said 3 is an answer; even though that is an extraneous root.  Why did it not give 3 when I told it to start at 2???

thanks

Bruce

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[John Hanna]

Bruce,

Take a look at the Newton’s Method iterations starting at each point. Some starting points can be ‘diabolical’.

 

What’s the function?

Regards,

         John

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[B Hartman]

I attached the tns file in my original post. 

[John Hanna]

Got it.In this screenshot, notice the difference:

 

… x, -0.499 indicates a lower bound for the search interval.

… x=-0.499 is an initial guess.

(I got this from the catalog syntax help)

 

So you are restricting the domain to exclude the only real root.

Still not sure why it returns 3 yet… stay tuned.

Regards,

         John

[John Hanna]

Why x=3?

Looking at the graph of each side of the equation, I see that f2 and f3 get ‘close to each other’ near x=3. Since nSolve is looking for a numeric approximation to the equation and you’ve eliminated the -.5 value by restricting the domain, the next best guess is x=3 because the values do get closer together as you approach x=3 (even though they’re really ‘large negative’ numbers – see a table).

 

If you use the simplified form of the expression things go better:

 

…but I could be wrong! (I also don’t think it’s using Newton’s Method).

Lesson: understand the device J

Regards,

         John