Gce Model Questions Vol1 2019 Further Mathematics Question 33

Practice objective / multiple choice question 33 from the 2019 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2019 Further Mathematics Objective / Multiple Choice Medium Difficulty
Question 33 GCE_MODEL_QUESTIONS_VOL1 • 2019 • FURTHER_MATHEMATICS • objective

The function \(f(x)=x^{3}e^{-x}\) is defined for all real \(x\). (i) Find all \(x\) at which the graph of \(f\) has a point of inflection. (ii) For each such \(x\), give the corresponding \(y\)-coordinate on the curve.

Answer Options

Correct Answer A. Inflection points: \(x=0\) with \(y=0\); \(x=3-\sqrt{3}\) with \(y=(3-\sqrt{3})^{3}e^{-(3-\sqrt{3})}\) (≈0.572); \(x=3+\sqrt{3}\) with \(y=(3+\sqrt{3})^{3}e^{-(3+\sqrt{3})}\) (≈0.931).
B. Inflection points: \(x=1\) with \(y=e^{-1}\); \(x=3-\sqrt{3}\) with \(y=(3-\sqrt{3})^{3}e^{-(3-\sqrt{3})}\) (≈0.572); \(x=3+\sqrt{3}\) with \(y=(3+\sqrt{3})^{3}e^{-(3+\sqrt{3})}\) (≈0.931).
C. Inflection points: \(x=0\) with \(y=0\); \(x=3-\sqrt{3}\) with \(y=(3-\sqrt{3})^{3}e^{-(3-\sqrt{3})}\) (≈0.400); \(x=3+\sqrt{3}\) with \(y=(3+\sqrt{3})^{3}e^{-(3+\sqrt{3})}\) (≈1.200).
D. Inflection points: \(x=0\) with \(y=0\); \(x=3-\sqrt{3}\) with \(y=(3-\sqrt{3})^{2}e^{-(3-\sqrt{3})}\) (≈0.572); \(x=3+\sqrt{3}\) with \(y=(3+\sqrt{3})^{2}e^{-(3+\sqrt{3})}\) (≈0.931).
Correct Answer
A
Correct Option:
Inflection points: \(x=0\) with \(y=0\); \(x=3-\sqrt{3}\) with \(y=(3-\sqrt{3})^{3}e^{-(3-\sqrt{3})}\) (≈0.572); \(x=3+\sqrt{3}\) with \(y=(3+\sqrt{3})^{3}e^{-(3+\sqrt{3})}\) (≈0.931).

About This Question

This is Gce Model Questions Vol1 2019 Further Mathematics Question 33. It is one of the objective questions from the 2019 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Medium .

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