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Questions › DSE › DSE 2011 › Q23
2 marksMathematics › Single-variable optimisation › Applied optimisationHardabout 3 min

DSE 2011 Question 23: Single-variable optimisation

The closest point on the parabola y=14x2y=\tfrac{1}{4}x^{2}y=41​x2 from a given point (0,b)(0,b)(0,b) on the vertical axis, with b>0b>0b>0, is the origin if and only if

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The closest point on the parabola y=1/4x² from a given point (0,b) on the vertical axis, with b>0, is the origin if and only if (A) b<3 (B) b>3 (C) b<2 (D) b>2

Also written as: The closest point on the parabola y=1/4x^2 from a given point (0,b) on the vertical axis, with b>0, is the origin if and only if

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

What this question tests

This question is on Applied optimisation, part of Single-variable optimisation in Mathematics.

Maximising profit, revenue or area and minimising cost or time in applied settings.

TestStop has 12 past-paper questions on this subtopic.

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Question from the DSE 2011 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.