Differentiation of trigonometric functions and differentiation rules — Question 87

Original QCE Vault practice · 5 marks

Q87 · Practice questionTechnology-freeComplex familiar5 marks

QUESTION 87 (5 marks)

For

f(x)=\sin x+\dfrac12\cos(2x)

0\le x\le\pi

, determine all interior stationary points.

WORKED SOLUTION

5 marks

ANSWER

x=\dfrac\pi6,\ \dfrac\pi2,\ \dfrac{5\pi}6

Worked solution

f'(x)=\cos x-\sin(2x)=\cos x(1-2\sin x)

. Hence

\cos x=0

gives

x=\pi/2

, and

\sin x=1/2

gives

x=\pi/6,5\pi/6

Differentiates the function correctly.

[1 mark]

Factors as

\cos x(1-2\sin x)

[1 mark]

Obtains

x=\pi/2

[1 mark]

Obtains

x=\pi/6

and

5\pi/6

[1 mark]

Reports all interior stationary points.

[1 mark]

Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.

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