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Coolmath Precalculus Review Calculus Preview
Lesson 13 - Graphing - More on Tangent Lines (page 3 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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Now, look at the tangent lines on the right side...
 

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

The slopes not only tell us that revenue is decreasing...  But, those values are getting smaller!  This is NOT a good thing when revenue is involved.

OK, let's look at one of those valleys:

Look at the tangent lines on the left...
 

on the decreasing side of a valley...  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
 

Things are bad...  But, although those slopes are negative, they're getting bigger.

This could mean that a much needed turnaround in revenue is coming!  Look at the bottom...  There's one of those horizontal tangent lines again!
 

at the bottom of a valley, the slope is 0
 

Continued on the next page

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

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