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)=x3 on [0,2].

1. 1.15
2. 1
3. 2
4. 0.58

Answer

A. 1.15

Solution

f'(c)=f(2)-f(0)/2-0= 82=4. Then 3c2=4 c=2/ 3 1.15.

More Rolle's Theorem and the Mean Value Theorem questions

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

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