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Questions › DSE › DSE 2010 › Q39
2 marksMathematics › Single-variable optimisation › Optimisation on a closed intervalHardabout 4 min

DSE 2010 Question 39: Single-variable optimisation

Setup, from Q38 of the paper:

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,

Consider fff as described in the previous question. Then,

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Plain-text version

Setup, from Q38 of the paper: 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, Consider f as described in the previous question. 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 the interval [a,b]

Also written as: Setup, from Q38 of the paper: 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, Consider f as described in the previous question. 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.