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daperkins
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Ok, so a secant line is one that touches a curve at two points. Still not sure the significance of a tangent line.
 3 years ago
 3 years ago
daperkins Group Title
Ok, so a secant line is one that touches a curve at two points. Still not sure the significance of a tangent line.
 3 years ago
 3 years ago

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FreeTrader Group TitleBest ResponseYou've already chosen the best response.2
If you keep moving one of the points on the curve closer and closer to the other fixed point, then the slope of the secant lines converges onto the tangent line. The tangent line is the instantaneous slope of the fixed point on the curve.
 3 years ago

daperkins Group TitleBest ResponseYou've already chosen the best response.0
I think I get it, somewhat. I'll keep hammering away. Thanks!
 3 years ago

FreeTrader Group TitleBest ResponseYou've already chosen the best response.2
daperkins, when you do the worked example in section 1, you will have the opportunity to check out the secant approximation mathlet tool located at http://ocw.mit.edu/courses/mathematics/1801scsinglevariablecalculusfall2010/partadefinitionandbasicrules/session1introductiontoderivatives/SecantApproximation.html which will provide a visual way to see the secant lines and the tangent line, and how they interact.
 3 years ago

FabianMontescu Group TitleBest ResponseYou've already chosen the best response.0
The way I like thinking about this is the following: you can only define a secant and a tangent in the neighborhood of a point in a function. Around a small interval in that neighborhood, a tangent will touch the function once and a secant will touch the function more than once. Therefore, lines that are tangents to a function on a given point may be secants (or not touch the function anymore) on other points. I hope that helps!
 3 years ago
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