The mean value theorem / Rolle's theorem Quiz

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10 questions. Calculator allowed. Show your working. steplyclass.com/calculus-1/the-mean-value-theorem-over-rolle-s-theorem/quiz/

1. 1

   Solve Rolle's theorem for f(x) = x² − 4x on [0, 4]
   1. A) c = 4
   2. B) c = 6
   3. C) c = 2
   4. D) c = 0

2. 2

   Solve Rolle's theorem for f(x) = x² + 2x on [−2, 0]

   Answer: ____________________

3. 3

   Find the mean value theorem for f(x) = x² on [1, 3].
   1. A) c = 9
   2. B) c = 1
   3. C) c = 4
   4. D) c = 2

4. 4

   Find the mean value theorem for f(x) = x² + 4x on [0, 2].

   Answer: ____________________

5. 5

   Find the mean value theorem for f(x) = x² − 6x + 1 on [0, 5].
   1. A) c ≈ 25
   2. B) c ≈ 1
   3. C) c ≈ 2.5
   4. D) c ≈ 5

6. 6

   Find c for the mean value theorem, f(x) = x³ − x on [0, 2]

   Answer: ____________________

7. 7

   Find the mean value theorem for f(x) = x³ − 2x on [0, 2].
   1. A) c ≈ 2
   2. B) c ≈ 4
   3. C) c ≈ 1.15
   4. D) c ≈ 0

8. 8

   Find c for the mean value theorem, f(x) = x³ + x on [−1, 2]

   Answer: ____________________

9. 9

   Find the mean value theorem for f(x) = x³ + 2x on [−2, 2].
   1. A) 6
   2. B) 4
   3. C) −1.15
   4. D) −12

10. 10

    Solve Rolle's theorem for f(x) = x³ − x on [0, 1]

    Answer: ____________________