A differentiable function satisfies f(2) = 5 and f(6) = 17. What value must f'(c) have for at least one c between 2 and 6?
Correct answer: B. 3
- A. 2
- B. 3
- C. 4
- D. 12
Explanation
The Mean Value Theorem states that some c in (2, 6) has f'(c) = [f(6) - f(2)]/(6 - 2). This equals (17 - 5)/4 = 3, so the required value is 3.
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