The function is twice differentiable, and , , . Then, it must be that:
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DSE 2019 Question 41: Limits, continuity and differentiability
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The function f(x) is twice differentiable, and f(2)=4, f(3)=9, f(4)=16. Then, it must be that: (A) f′′(x)=3 for some x∈(2,4) (B) f′′(x)=4 for some x∈(2,3) (C) f′′(x)=3 for some x∈(2,3) (D) f′′(x)=2 for some x∈(2,4)
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What this question tests
This question is on Mean value theorem and Rolle's theorem, part of Limits, continuity and differentiability in Mathematics.
Results linking the average rate of change to a derivative at some point.
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