# Second Derivatives and Beyond

### Topics

## Introduction to Second Derivatives And Beyond - At A Glance:

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: