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Topic: [ap-calculus] Definition of tangent line
Replies: 2   Last Post: Oct 16, 2010 10:22 PM

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BCrombie@AOL.COM

Posts: 108
Registered: 12/8/04
Re: [ap-calculus] Definition of tangent line
Posted: Oct 16, 2010 10:22 PM
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In Book III, Proposition 16 of the Elements Euclid defines the tangent to a
circle:

"The straight line drawn at right angles to the diameter of a circle from
its extremity will fall outside the circle, and into the space between the
straight line and the circumference another straight line cannot be
interposed."

Modern translation: The tangent line through a point on a curve is the
closest line to the curve at that point.

Bill

In a message dated 10/15/2010 9:54:59 P.M. Eastern Daylight Time,
nswenson@masterschool.org writes:

One of my students hit me today with a question I couldn't answer, so I
thought I would ask you brilliant people out there for some help. The
definition that we have been using for a tangent line is, "A line which intersects
the curve at exactly one point." However, the function they were dealing
with was a cubic function. They had to determine the points at which there
were horizontal tangents. Her reasoning was that there were no horizontal
tangents, since any line that hit the graph horizontally would cross at more
than one point. How do I need to redifine tangent line to eliminate this
very insightful answer?
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http://apcentral.collegeboard.com/calculusbc
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