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

Find the value of c guaranteed by the Mean Value Theorem for f(x)= x on [1,9].

1. 5
2. 4
3. 3
4. 2

Answer

B. 4

Solution

f'(c)=3-1/9-1= 14 and f'(c)=1/2 c. So c=2 c=4.

More Rolle's Theorem and the Mean Value Theorem questions

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

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