A rectangle has its lower left hand corner at the origin and its upper right hand corner on the graph of . For which is the area of the rectangle minimized?
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DSE 2012 Question 48: Single-variable optimisation
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A rectangle has its lower left hand corner at the origin and its upper right hand corner on the graph of f(x)=x²+(1/x²). For which x is the area of the rectangle minimized? (A) x=0 (B) x=∞ (C) x=(1/3)^(1/4) (D) x=2^(1/3)
Also written as: A rectangle has its lower left hand corner at the origin and its upper right hand corner on the graph of f(x)=x^2+(1/x^2). For which x is the area of the rectangle minimized?
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.
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