Do things improve?  Yep!  (Whew.)

Look at the tangent lines on the right...

on the increasing side of a valley...  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

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.

a mountain

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:

on a mountain, the slopes are positive to the left of the top and negative to the right of the top

Here's the list in order from left to right:

4 / 3 , 1 , 2 / 3 , 2 / 7 , 0 , -2 / 7 , -2 / 3 , -1 , -4 / 3

Notice that the slopes of the tangent lines are decreasing.