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Questions › JNU › JNU SSS 2012 › Q63
1 mark, −0.25Mathematics › Single-variable optimisation › Optimisation on a closed intervalModerateabout 2 min

JNU SSS 2012 Question 63: Single-variable optimisation

Let fff be a twice differentiable real-valued function defined on the set of all real numbers greater than or equal to 0 and less than or equal to 1. Suppose fff attains the maximum value in its domain at x∗x^*x∗. Which of the following must be true?

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Let f be a twice differentiable real-valued function defined on the set of all real numbers greater than or equal to 0 and less than or equal to 1. Suppose f attains the maximum value in its domain at x*. Which of the following must be true? (A) f′(x*) = 0 (B) f′′(x*) < 0 (C) x* = 0 or x* = 1 or f′(x*) = 0 (D) None of the above

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.