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Questions › DSE › DSE 2016 › Q16
0 marksMathematics › Single-variable optimisation › Unconstrained extrema and the first- and second-order conditionsModerateabout 2 min

DSE 2016 Question 16: Single-variable optimisation

Consider f:R→Rf:\mathbb{R}\to\mathbb{R}f:R→R defined by f(x)=∑i=111∣x−ai∣f(x)=\sum_{i=1}^{11}|x-a_{i}|f(x)=∑i=111​∣x−ai​∣ for all x∈Rx\in\mathbb{R}x∈R, where a1<…<a11a_{1}<\ldots<a_{11}a1​<…<a11​. This function has a minimum when xxx equals:

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Consider f:ℝ→ℝ defined by f(x)=Σᵢ₌₁¹¹|x-aᵢ| for all x∈ℝ, where a₁<…<a₁₁. This function has a minimum when x equals: (A) a₂ (B) a₆ (C) a₇ (D) a₁₁

Also written as: Consider f:R->R defined by f(x)= sum_(i=1)^(11)|x-a_i| for all x in R, where a_1<...<a_(11). This function has a minimum when x equals:

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

What this question tests

This question is on Unconstrained extrema and the first- and second-order conditions, part of Single-variable optimisation in Mathematics.

Finding and classifying maxima and minima using derivatives.

TestStop has 12 past-paper questions on this subtopic.

Practise Single-variable optimisationMore on Unconstrained extrema and the first- and second-order conditions

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Question from the DSE 2016 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.