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Questions › DSE › DSE 2018 › Q5
4 marks, −1Mathematics › Limits, continuity and differentiability › Mean value theorem and Rolle's theoremHardabout 3 min

DSE 2018 Question 5: Limits, continuity and differentiability

Let f:[0,1]→Rf : [0,1] \to \mathbb{R}f:[0,1]→R be twice differentiable. Suppose that the line segment joining the points (0,f(0))(0, f(0))(0,f(0)) and (1,f(1))(1, f(1))(1,f(1)) intersects the graph of fff at a point (a,f(a))(a, f(a))(a,f(a)), where 0<a<10 < a < 10<a<1. Then,

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Let f: [0,1] → ℝ be twice differentiable. Suppose that the line segment joining the points (0, f(0)) and (1, f(1)) intersects the graph of f at a point (a, f(a)), where 0 < a < 1. Then, (A) there exists z ∈ [0,1] such that f′(z) = 0 (B) there exists z ∈ [0,1] such that f′′(z) = |f(1) - f(0)| (C) there exists z ∈ [0,1] such that f′′(z) = f(1) - f(0) (D) there exists z ∈ [0,1] such that f′′(z) = 0

Also written as: Let f: [0,1] -> R be twice differentiable. Suppose that the line segment joining the points (0, f(0)) and (1, f(1)) intersects the graph of f at a point (a, f(a)), where 0 < a < 1. Then,

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

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.

TestStop has 13 past-paper questions on this subtopic.

Practise Limits, continuity and differentiabilityMore on Mean value theorem and Rolle's theorem

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Question from the DSE 2018 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.