- 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

If *f *" is positive, then *f* is concave up. If *f *" is negative, then *f* is concave down. If *f *" is zero, we say that the function *f* has *no concavity*. It's flat. Pancakes can survive in a world of no concavity. When a function has no concavity, it means *f* doesn't curve at all. It's a straight line:

Exercise 1

Determine if the function is concave up, concave down, or has no concavity:

Exercise 2

Determine if the function is concave up, concave down, or has no concavity:

Exercise 3

Determine if the function is concave up, concave down, or has no concavity:

Exercise 4

Determine if the function is concave up, concave down, or has no concavity:

Exercise 5

Determine if the function is concave up, concave down, or has no concavity:

Exercise 6

Determine if the function is concave up, concave down, or has no concavity:

Exercise 7

Determine if the function is concave up, concave down, or has no concavity:

Exercise 8

Determine if the function is concave up, concave down, or has no concavity:

Exercise 9

Determine if the function is concave up, concave down, or has no concavity:

Exercise 10

Determine if the function is concave up, concave down, or has no concavity: