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Questions › DSE › DSE 2010 › Q38
2 marksMathematics › Single-variable optimisation › Optimisation on a closed intervalHardabout 4 min

DSE 2010 Question 38: Single-variable optimisation

Consider a twice differentiable function f:ℜ→ℜf:\Re\to\Ref:ℜ→ℜ and a,b∈ℜa,b\in\Rea,b∈ℜ with a<ba<ba<b, f(a)=0=f(b)f(a)=0=f(b)f(a)=0=f(b) and D2f(x)+Df(x)−1=0D^{2}f(x)+Df(x)-1=0D2f(x)+Df(x)−1=0 for every x∈[a,b]x\in[a,b]x∈[a,b]. Then,

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Consider a twice differentiable function f:ℜ→ℜ and a,b∈ℜ with a<b, f(a)=0=f(b) and D²f(x)+Df(x)-1=0 for every x∈[a,b]. Then, (A) f has a maximum but not a minimum over the open interval (a,b) (B) f has a minimum but not a maximum over (a,b) (C) f has neither a maximum nor a minimum over (a,b) (D) f has a maximum and a minimum over (a,b)

Also written as: Consider a twice differentiable function f: Re -> Re and a,b in Re with a<b, f(a)=0=f(b) and D^2f(x)+Df(x)-1=0 for every x in [a,b]. Then,

Single-variable optimisation has come up 37 times in 6 exams since 2010.

What this question tests

This question is on Optimisation on a closed interval, part of Single-variable optimisation in Mathematics.

Global maxima and minima when the domain is bounded, including endpoints and existence.

TestStop has 13 past-paper questions on this subtopic.

Practise Single-variable optimisationMore on Optimisation on a closed interval

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Question from the DSE 2010 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.