The Mean Value Theorem

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari finds the c from the Mean Value Theorem for f(x) = x³ − 7x on 0 ≤ x ≤ 3. What is c, to the nearest hundredth?

   1.73
2. 2.

   Bo finds the c from the Mean Value Theorem for f(x) = x³ + 4x on 0 ≤ x ≤ 7. What is c, to the nearest hundredth?

   4.04
3. 3.

   Esme finds the c from the Mean Value Theorem for f(x) = x³ − 5x on 0 ≤ x ≤ 2. What is c, to the nearest hundredth?

   1.15
4. 4.

   Jun finds the c from the Mean Value Theorem for f(x) = x³ + 2x on 0 ≤ x ≤ 5. What is c, to the nearest hundredth?

   2.89
5. 5.

   A drone moves smoothly from 5 km along its route at t = 0 h to 101 km at t = 6 h. What speed, in km/h, must Luz see it reach at some moment?

   16
6. 6.

   A boat moves smoothly from 12 km along its route at t = 0 h to 51 km at t = 3 h. What speed, in km/h, must Milo see it reach at some moment?

   13
7. 7.

   A bus moves smoothly from 20 km along its route at t = 0 h to 140 km at t = 8 h. What speed, in km/h, must Noah see it reach at some moment?

   15
8. 8.

   f(x) = x² − 6x + 4 has f(1) = f(5). Pia finds the c in 1 < x < 5 that Rolle's theorem promises. What is c?

   3
9. 9.

   f(x) = x² − 8x + 1 has f(1) = f(7). Ren finds the c in 1 < x < 7 that Rolle's theorem promises. What is c?

   4
10. 10.

    f(x) = x² − 10x + 10 has f(4) = f(6). Zee finds the c in 4 < x < 6 that Rolle's theorem promises. What is c?

    5