For the real-valued function (defined for all real numbers ), the point is
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DSE 2011 Question 1: Single-variable optimisation
Answer and worked solution
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Plain-text version
For the real-valued function f(x)=x⁴-4x³+6x²-4x+1 (defined for all real numbers x), the point x=1 is (A) a local minimum. (B) a local maximum. (C) a point of inflection. (D) none of the above.
Also written as: For the real-valued function f(x)=x^4-4x^3+6x^2-4x+1 (defined for all real numbers x), the point x=1 is
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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Question from the DSE 2011 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.