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[apcalculus] RE: implicit differentiation problem...
Posted:
Oct 12, 2004 11:08 AM


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: APCalculus Subject: [apcalculus] 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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