Neco 2017 Further Mathematics Question 30

Practice objective / multiple choice question 30 from the 2017 Neco Further Mathematics examination.

Neco 2017 Further Mathematics Objective / Multiple Choice Medium Difficulty
Question 30 NECO • 2017 • FURTHER_MATHEMATICS • objective

For the function \(f(x)=x^{3}-6x^{2}+9x+2\):\n(a) Find all stationary points and classify each as a local maximum, local minimum, or point of inflection.\n(b) Write the equation of the tangent line at the point where \(f\) attains its maximum.\n(c) Evaluate the definite integral \(\displaystyle\int_{x_{1}}^{x_{2}} f(x)\,dx\) where \(x_{1}\) and \(x_{2}\) are the abscissas of the two stationary points.

Answer Options

A. Maximum at (0,2), minimum at (3,2); tangent line y=2; \\(\\int_{0}^{3}f(x)dx=5\\)
B. Maximum at (1,6), minimum at (3,2); tangent line y=5; \\(\\int_{1}^{3}f(x)dx=7\\)
C. Maximum at (2,8), minimum at (4,0); tangent line y=8; \\(\\int_{2}^{4}f(x)dx=10\\)
Correct Answer D. Maximum at (1,6), minimum at (3,2); tangent line y=6; \(\int_{1}^{3}f(x)dx=8\)
Correct Answer
D
Correct Option:
Maximum at (1,6), minimum at (3,2); tangent line y=6; \(\int_{1}^{3}f(x)dx=8\)

About This Question

This is Neco 2017 Further Mathematics Question 30. It is one of the objective questions from the 2017 Neco Further Mathematics examination.

Difficulty level: Medium .

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