Suppose that is a twice differentiable function and ; ; . Which of the following is necessarily true? (First and second derivatives of are and respectively.)
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DSE 2016 Question 15: Limits, continuity and differentiability
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Suppose that g(x) is a twice differentiable function and g(1)=1; g(2)=4; g(3)=9. Which of the following is necessarily true? (First and second derivatives of g are g′ and g′′ respectively.) (A) g′′(x)=3 for some x∈[1,2] (B) g′′(x)=5 for some x∈[2,3] (C) g′′(x)=2 for some x∈[1,3] (D) g′′(x)=2 for some x∈[1.5,2.5]
Also written as: Suppose that g(x) is a twice differentiable function and g(1)=1; g(2)=4; g(3)=9. Which of the following is necessarily true? (First and second derivatives of g are g' and g'' respectively.)
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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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Question from the DSE 2016 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.