### All AP Calculus AB Resources

## Example Questions

### Example Question #1 : Second Derivatives

What is the concavity of at x=1?

**Possible Answers:**

Concave Up

No Concavity

Concave Diagonal

Concave Horizontal

Concave Down

**Correct answer:**

Concave Up

Explanation:

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 #2 : Second Derivatives

Find the second derivative.

**Possible Answers:**

**Correct answer:**

Explanation:

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:**

Explanation:

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

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #5 : Second Derivatives

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #6 : Second Derivatives

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #7 : Second Derivatives

**Possible Answers:**

**Correct answer:**

Explanation:

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

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #9 : Second Derivatives

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #10 : Second Derivatives

**Possible Answers:**

**Correct answer:**

Explanation:

Jaroslaw

Certified Tutor

Certified Tutor

Heriot Watt University, Master of Science, Physics. Heriot Watt University, Doctor of Science, Theoretical and Mathematical P...

### All AP Calculus AB Resources

Popular Subjects

Computer Science Tutoring in New York City, GMAT Tutoring in Atlanta, Math Tutoring in San Diego, Computer Science Tutoring in Los Angeles, Physics Tutoring in San Diego, Math Tutoring in Washington DC, ACT Tutoring in Seattle, LSAT Tutoring in San Diego, Reading Tutoring in Denver, Calculus Tutoring in Houston
Popular Courses & Classes

GMAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Houston, MCAT Courses & Classes in Miami, SAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Boston, GRE Courses & Classes in Los Angeles, LSAT Courses & Classes in Seattle, SSAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Boston