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Specialist Maths — Question 11

QCAA 2021, Paper 1 · 5 marks

Q11 · 2021 · Technology-freeSimple familiar5 marks

QUESTION 11 (5 marks)

Let f(x)=tan⁡−1(x2)f(x)=\tan^{-1}\left(\dfrac{x}{2}\right) for suitable values of xx, where f(x)∈(−π/2,π/2)f(x)\in(-\pi/2,\pi/2).
a)
Determine f(2)f(2).
[1 mark]
b)
Determine f′(2)f'(2).
[2 marks]
c)
Use the results from Questions 11a) and 11b) to determine the equation of the tangent to the graph of y=f(x)y=f(x) at x=2x=2.
[2 marks]
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