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Do things improve? Yep!
(Whew.)
Look at the tangent lines on the
right...
Not only are those slopes
positive, they are getting bigger. This is when you start
celebrating!
In Calculus, you'll be doing a lot
of hunting for those horizontal tangent lines because that's where
interesting stuff happens: maximums, minimums, changing from
increasing to decreasing and changing from decreasing to increasing.
While we're here, I want to point
out a couple more things to you.
Look at the mountain again.
Notice that it's shaped like an
upside down bowl... In Calculus, you'll call this "concave
down." Let's take another look at those slopes:
Here's the list in order from left
to right:
Notice that the slopes of the
tangent lines are decreasing.
Continued on the
next
page
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