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Topic: [ap-calculus] RE: implicit differentiation problem...
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Pat ballew

Posts: 455
Registered: 12/3/04
[ap-calculus] RE: implicit differentiation problem...
Posted: Oct 12, 2004 11:08 AM
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Maybe this will do it..
The curve is symmetric in the line y=x , so the slope at (p,q) is the
reciprocal of the slope at (q,p)... And at any point (p,p) either the slope
is its own reciprocal, (as it is at (4.5,4.50) where the slope must be -1 )
or it must have two tangents at that point (or none)..


Pat Ballew
Lakenheath, UK

MathWords http://www.pballew.net/etyindex.html


-----Original Message-----
From: David DeMarchis [mailto://ddemarchis@canterburyschool.org]
Sent: Monday, October 11, 2004 2:45 PM
To: AP-Calculus
Subject: [ap-calculus] implicit differentiation problem...

The following curve x^3 + y^3 - 9xy = 0 (appearing on page 149 of Calculus
- Finney DeMana Waits Kennedy) has both a horizontal and vertical tangent at
the origin. However, implicit differentiation doesn't seem to reveal this
as y' ends up giving you 0/0 at the origin. Can anyone shed some light on
this and whether or not there is a way to see that the curve in fact as both
a vertical and horizontal tangent at the origin by looking at the
derivative? Thanks David DeMarchis Canterbury School Fort Wayne, IN

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