Derivative of a linear function plus a cosine term and the equation of a tangent at an exact radian value
Derivative of a linear function plus a cosine term and the equation of a tangent at an exact radian value
6 marks
A curve \(C\) has equation \(y=4x-3\cos x\), where \(x\in\mathbb{R}\).
- Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\).[2]
- Hence, at the point on \(C\) where \(x=\dfrac{\pi}{2}\), find an equation of the tangent line in the form \(y=mx+c\).[4]
Solution:
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Answer:(a) \(\dfrac{\mathrm{d}y}{\mathrm{d}x}=4+3\sin x\) (b) \(y=7x-\dfrac{3\pi}{2}\)
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