Rolle's Theorem and the Mean Value Theorem — Engineering Board Exam Practice Questions

4 free engineering board exam reviewer questions on Rolle's Theorem and the Mean Value Theorem (Differential Calculus), each with the correct answer and a worked solution.

1. Which function does NOT satisfy the hypotheses of Rolle's Theorem on [-1,1]?
2. Find the value of c guaranteed by the Mean Value Theorem for f(x)= x on [1,9].
3. Find the value of c guaranteed by the Mean Value Theorem for f(x)=x3 on [0,2].
4. Find the value of c guaranteed by Rolle's Theorem for f(x)=x2-4x+3 on [1,3].