# Second Derivatives and Beyond

# Concave Up Exercises

### Example 1

Determine if the statement is equivalent to (mean the same thing as) the statement

"*f* is concave up."

Explain your answer (whether the statement is equivalent or not).

*f* is increasing.

### Example 2

Determine if the statement is equivalent to (mean the same thing as) the statement

"*f* is concave up."

Explain your answer (whether the statement is equivalent or not).

*f* is positive.

### Example 3

Determine if the statement is equivalent to (mean the same thing as) the statement

"*f* is concave up."

Explain your answer (whether the statement is equivalent or not).

*f *' is increasing.

### Example 4

Determine if the statement is equivalent to (mean the same thing as) the statement

"*f* is concave up."

Explain your answer (whether the statement is equivalent or not).

*f *' is positive.

### Example 5

Determine if the statement is equivalent to (mean the same thing as) the statement

"*f* is concave up."

Explain your answer (whether the statement is equivalent or not).

*f *" is increasing.

### Example 6

Determine if the statement is equivalent to (mean the same thing as) the statement

"*f* is concave up."

Explain your answer (whether the statement is equivalent or not).

*f *" is positive.