Suppose is a given positive real number. The equation must have a solution if
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2 marks, −0.666666666666667MathematicsSingle-variable optimisationUnconstrained extrema and the first- and second-order conditionsModerateabout 2 min
DSE 2014 Question 27: Single-variable optimisation
Answer and worked solution
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Plain-text version
Suppose c is a given positive real number. The equation ln x=cx² must have a solution if (A) c<1/(2e) (B) c<1/e (C) c>1/(2e) (D) c>1/e
Also written as: Suppose c is a given positive real number. The equation ln x=cx^2 must have a solution if
Single-variable optimisation has come up 37 times in 6 exams since 2010.
What this question tests
This question is on Unconstrained extrema and the first- and second-order conditions, part of Single-variable optimisation in Mathematics.
Finding and classifying maxima and minima using derivatives.
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