The mean value theorem / Rolle's theorem Quiz
10 questions · easy to harder · Calculus 1 · score and step-by-step answers
How it works
- 10 questions, about 30 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 5 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise the lesson with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
1 Question 1
Solve Rolle's theorem for f(x) = x2 − 4x on [0, 4]- A) c = 4
- B) c = 6
- C) c = 2
- D) c = 0
2 Question 2
Solve Rolle's theorem for f(x) = x2 + 2x on [−2, 0]Type the answer.
3 Question 3
Find the mean value theorem for f(x) = x2 on [1, 3].- A) c = 9
- B) c = 1
- C) c = 4
- D) c = 2
4 Question 4
Find the mean value theorem for f(x) = x2 + 4x on [0, 2].Type the answer.
5 Question 5
Find the mean value theorem for f(x) = x2 − 6x + 1 on [0, 5].- A) c ≈ 25
- B) c ≈ 1
- C) c ≈ 2.5
- D) c ≈ 5
6 Question 6
Find c for the mean value theorem, f(x) = x3 − x on [0, 2]Type the answer.
7 Question 7
Find the mean value theorem for f(x) = x3 − 2x on [0, 2].- A) c ≈ 2
- B) c ≈ 4
- C) c ≈ 1.15
- D) c ≈ 0
8 Question 8
Find c for the mean value theorem, f(x) = x3 + x on [−1, 2]Type the answer.
9 Question 9
Find the mean value theorem for f(x) = x3 + 2x on [−2, 2].- A) 6
- B) 4
- C) −1.15
- D) −12
10 Question 10
Solve Rolle's theorem for f(x) = x3 − x on [0, 1]Type the answer.