### All AP Calculus AB Resources

## Example Questions

### Example Question #1 : Second Derivatives

What is the concavity of at x=1?

**Possible Answers:**

Concave Up

Concave Diagonal

Concave Down

Concave Horizontal

No Concavity

**Correct answer:**

Concave Up

First, find the double derivative of the function given.

You should get .

Next, plug in x=1 to get .

The double derivative is a positive number, which means the concavity is Concave Up.

### Example Question #1 : Relationship Between The Concavity Of ƒ And The Sign Of ƒ''

Find the second derivative.

**Possible Answers:**

**Correct answer:**

We need to find the second derivative. To do this we will use power rule twice. We will take the first derivative by power rule, then the second derivative by power rule once again. Power rule says that we take the exponent of the “x” value and bring it to the front. Then we subtract one from the exponent.

Therefore, the first derivative is and the second derivative is by power rule.

### Example Question #3 : Second Derivatives

**Possible Answers:**

**Correct answer:**

### Example Question #2 : Relationship Between The Concavity Of ƒ And The Sign Of ƒ''

**Possible Answers:**

**Correct answer:**

### Example Question #3 : Relationship Between The Concavity Of ƒ And The Sign Of ƒ''

**Possible Answers:**

**Correct answer:**

### Example Question #4 : Relationship Between The Concavity Of ƒ And The Sign Of ƒ''

**Possible Answers:**

**Correct answer:**

### Example Question #7 : Second Derivatives

**Possible Answers:**

**Correct answer:**

### Example Question #5 : Relationship Between The Concavity Of ƒ And The Sign Of ƒ''

**Possible Answers:**

**Correct answer:**

### Example Question #6 : Relationship Between The Concavity Of ƒ And The Sign Of ƒ''

**Possible Answers:**

**Correct answer:**

### Example Question #7 : Relationship Between The Concavity Of ƒ And The Sign Of ƒ''

**Possible Answers:**

**Correct answer:**

### All AP Calculus AB Resources

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