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Questions › DSE › DSE 2012 › Q46
2 marksMathematics › Single-variable optimisation › Unconstrained extrema and the first- and second-order conditionsHardabout 4 min

DSE 2012 Question 46: Single-variable optimisation

What is the total number of local maxima and local minima of the following function f(x)={(2+x)3if −3<x≤−1x2/3if −1<x<2f(x)=\begin{cases}(2+x)^{3} & \text{if }-3<x\le -1\\ x^{2/3} & \text{if }-1<x<2\end{cases}f(x)={(2+x)3x2/3​if −3<x≤−1if −1<x<2​

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What is the total number of local maxima and local minima of the following function f(x)={ (2+x)³ if -3<x≤ -1; x^(2/3) if -1<x<2 } (A) 1 (B) 2 (C) 3 (D) 4

Also written as: What is the total number of local maxima and local minima of the following function f(x)={ (2+x)^3 if -3<x<= -1; x^(2/3) if -1<x<2 }

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.

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Question from the DSE 2012 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.