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Questions › DSE › DSE 2015 › Q38
2 marks, −0.666666666666667Mathematics › Difference and differential equations › Stability and phase diagramsHardabout 4 min

DSE 2015 Question 38: Difference and differential equations

Suppose f:[0,1]→Rf:[0,1]\to\mathbb{R}f:[0,1]→R is twice differentiable with f′′(x)+f′(x)=1f''(x)+f'(x)=1f′′(x)+f′(x)=1 for all x∈(0,1)x\in(0,1)x∈(0,1) and f(0)=0=f(1)f(0)=0=f(1)f(0)=0=f(1). Then

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Suppose f:[0,1]→ℝ is twice differentiable with f′′(x)+f′(x)=1 for all x∈(0,1) and f(0)=0=f(1). Then (A) f does not attain positive values over (0,1) (B) f does not attain negative values over (0,1) (C) f attains positive and negative values over (0,1) (D) f is constant over (0,1)

Also written as: Suppose f:[0,1]->R is twice differentiable with f''(x)+f'(x)=1 for all x in (0,1) and f(0)=0=f(1). 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.

TestStop has 8 past-paper questions on this subtopic.

Practise Difference and differential equationsMore on Stability and phase diagrams

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Question from the DSE 2015 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.