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Questions › DSE › DSE 2017 › Q26
2 marks, −0.666666666666667Mathematics › Difference and differential equations › Stability and phase diagramsHardabout 4 min

DSE 2017 Question 26: Difference and differential equations

Let f:R→Rf:\mathbb{R}\to\mathbb{R}f:R→R be twice differentiable, with a<ba<ba<b, f(a)=0=f(b)f(a)=0=f(b)f(a)=0=f(b), and f′′(x)+f′(x)−1=0f''(x)+f'(x)-1=0f′′(x)+f′(x)−1=0 for every x∈[a,b]x\in[a,b]x∈[a,b]. Then

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Let f:ℝ→ℝ be twice differentiable, with a<b, f(a)=0=f(b), and f′′(x)+f′(x)-1=0 for every x∈[a,b]. Then (A) f(x)≤ 0 for every x∈[a,b] (B) f(x)≥ 0 for every x∈[a,b] (C) f(x)=0 for every x∈[a,b] (D) f must take positive and negative values on [a,b]

Also written as: Let f:R->R be twice differentiable, with a<b, f(a)=0=f(b), and f''(x)+f'(x)-1=0 for every x in [a,b]. Then

Difference and differential equations has come up 20 times in 5 exams since 2014.

What this question tests

This question is on Stability and phase diagrams, part of Difference and differential equations in Mathematics.

Whether solutions settle to an equilibrium and how to read the phase line.

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Practise Difference and differential equationsMore on Stability and phase diagrams

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Question from the DSE 2017 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.