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Questions › JNU › JNU SSS 2012 › Q96
1 mark, −0.25Mathematics › Single-variable optimisation › Optimisation on a closed intervalModerateabout 2 min

JNU SSS 2012 Question 96: Single-variable optimisation

Suppose f(x)=a1x+a2+(a3/x)f(x) = a_1 x + a_2 + (a_3 / x)f(x)=a1​x+a2​+(a3​/x), where a1a_1a1​, a2a_2a2​ and a3a_3a3​ are positive constants and xxx is assumed to take only positive values. Which of the following statements is true?

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Plain-text version

Suppose f(x) = a₁ x + a₂ + (a₃ / x), where a₁, a₂ and a₃ are positive constants and x is assumed to take only positive values. Which of the following statements is true? (A) f(x) has a minimum value but no maximum value (B) f(x) has a maximum value but no minimum value (C) f(x) has neither a minimum value nor a maximum value (D) f(x) has both a minimum value and a maximum value

Also written as: Suppose f(x) = a_1 x + a_2 + (a_3 / x), where a_1, a_2 and a_3 are positive constants and x is assumed to take only positive values. Which of the following statements is true?

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 JNU SSS 2012 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.