Engineering Board Exam Reviewer · Rolle's Theorem and the Mean Value Theorem · medium

Find the value of c guaranteed by Rolle's Theorem for f(x)=x2-4x+3 on [1,3].

1. 1
2. 3
3. 1.5
4. 2

Answer

D. 2

Solution

f(1)=f(3)=0. Rolle's Theorem gives f'(c)=2c-4=0 c=2, which lies in (1,3).

More Rolle's Theorem and the Mean Value Theorem questions

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].

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