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Questions › DSE › DSE 2013 › Q23
2 marksMathematics › Single-variable optimisation › Optimisation on a closed intervalHardabout 3 min

DSE 2013 Question 23: Single-variable optimisation

Consider f(x)=92x2/3−35x5/3f(x)=\tfrac92x^{2/3}-\tfrac35x^{5/3}f(x)=29​x2/3−53​x5/3 for all xxx in [−1,5][-1,5][−1,5]. f(5)f(5)f(5) is approximately 4.3864.3864.386. fff attains a maximum on [−1,5][-1,5][−1,5] at:

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Plain-text version

Consider f(x)=9/2x^(2/3)-3/5x^(5/3) for all x in [-1,5]. f(5) is approximately 4.386. f attains a maximum on [-1,5] at: (A) x=-1. (B) x=2. (C) x=3. (D) x=4.

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 2013 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.