🚀 go-pugleaf

Previously Larry Jones wrote:

>I am using a Calculus Text titled Elements of Calculus and Analytic
>Geometry by Thomas and Finney, published by Addison-Wesley,  c 1989.  On
>page 100, problem 34, the problem states " A line is drawn tangent to the
>curve y=x^3-x at the point (-1,0).  Where else does the line intersect
>the curve?"  I decided to use my TI-82 calculator to assist in solving
>this problem.  I entered y1 = x^3-x and after taking the derivative by
>hand and subbing in x=-1 to get a slope of 2 for the tangent line, I
>entered y2 = 2x+2.  I graphed both y1 and y2 using zoom 6.  Then 2nd Calc
>5 to determine intersection points.  I find the point (2,6) as an
>intersection point, but try as I may, I cannot get (-1,0), the original
>tangent line point, as an intersection point using 2nd Calc 5.  What am I
>doing wrong?
>		Thanks, Larry Jones
>				jonesl@calvin.duq.edu
>

I thought that the numerical used methods by the calculator were independent of
the graphing window.  Apparently not.  I duplicated your steps and produced
a similar result.  However, as soon as I set Xmax to 1.99 (or less) the
intersection calculation worked (with a guess < -1).  I also experimented
with finding the root of Y1-Y2 and, depending on the window, would
occasionally generate a NO SIGN CHANGE error.  While the TI archive has
texts on various numerical methods, I did not find one on how the TI finds
the intersection.  Does it simply subtract one function from the other and
then proceed to find the root?

I hope this has been of some help.

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Marc Dancer			Voice (413)-774-6269
Deerfield Academy		FAX   (413)-774-6629
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