- Topics At a Glance
- Second Derivatives via Formulas
- Third Derivatives and Beyond
- Concavity
- Concave Up
- Concave Down
- No Concavity
**Special Points**- Critical Points
- Points of Inflection
- Extreme Points and How to Find Them
- Finding & Classifying Extreme Points
- First Derivative Test
- Second Derivative Test
- Local vs. Global Points
- Using Derivatives to Draw Graphs
- Finding Points
- Finding Shapes
- Connecting the Dots
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

Special points are those random points awarded to the guy who invited us over to play board games. Blast you, house rules. They never seem to work in our favor.

In derivative land, if we have a function *f* whose first two derivatives exist (at least most of the time), there are some special types of points that we need to be able to find. Remember that the roots of a function are those *x*-values where the function value is equal to zero.

**Be Careful:** We use the word "point" in these sections to refer to an *x*-coordinate all by itself. When it comes time to graph things, we will need to find both the *x* and *y* coordinates in order to have a point that we can graph.