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Coolmath Precalculus Review Calculus Preview
Lesson 13 - Graphing - More on Tangent Lines (page 2 of 6)
---- This Precalculus review (Calculus preview) lesson covers more on how tangent lines are used in Calculus: concave up, concave down and points of inflection.

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Let's check out one of the mountains on the graph:
 

on the increasing side of a mountain...  the first tangent line has a slope of 4/3...  the second tangent line has a slope of 1...  the third tangent line has a slope of 2/3...  the fourth tangent line has a slope of 2/7
 

Look at what's happening to the slopes on the left side...  Yeah, they are positive... which means that the graph is increasing...  But, their values are getting smaller as you climb the mountain from left to right.  If I'm smart, I see that a revenue problem could be coming up!  Look at the top...
 

a tangent line on the very top of a mountain has a slope of 0
 

That's a horizontal tangent line.  It could mean that a big change is coming.  Yeah, it could mean that this will happen:
 

after hitting a slope of zero, the graph could continue to increase
 

But, unfortunately, that's not what happens here.

Continued on the next page

 The printing and distribution and/or downloading of these lessons is strictly prohibited.

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