The Mean Value Theorem

Answer Key - Grade 12 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   For f(x) = x³ − 2x on 0 ≤ x ≤ 3, the Mean Value Theorem promises a c with f′(c) equal to one number. Ari finds that number. What is it?

   7
2. 2.

   For f(x) = x³ + 3x on 1 ≤ x ≤ 3, the Mean Value Theorem promises a c with f′(c) equal to one number. Bo finds that number. What is it?

   16
3. 3.

   For f(x) = x³ + 5x on -2 ≤ x ≤ 1, the Mean Value Theorem promises a c with f′(c) equal to one number. Jun finds that number. What is it?

   8
4. 4.

   Luz finds the c from the Mean Value Theorem for f(x) = x² − 6x on 1 ≤ x ≤ 4. What is c?

   5/2
5. 5.

   Milo finds the c from the Mean Value Theorem for f(x) = x² + 5x on -1 ≤ x ≤ 4. What is c?

   3/2
6. 6.

   Noah finds the c from the Mean Value Theorem for f(x) = x² − 2x on 3 ≤ x ≤ 8. What is c?

   11/2
7. 7.

   Pia finds the c from the Mean Value Theorem for f(x) = 8/x on 1 ≤ x ≤ 4. What is c?

   2
8. 8.

   Ren finds the c from the Mean Value Theorem for f(x) = 12/x on 2 ≤ x ≤ 8. What is c?

   4
9. 9.

   Tala finds the c from the Mean Value Theorem for f(x) = 9/x on 1 ≤ x ≤ 9. What is c?

   3
10. 10.

    Zee finds the c from the Mean Value Theorem for f(x) = 24/x on 4 ≤ x ≤ 9. What is c?

    6