The diagram shows part of the curve with equation $$\[ y=4 \sin ^{2} x+8 \sin x+3, \]$$ where $$\(x\)$$ is measured in radians. The curve crosses the $$\(x\)$$-axis at the point $$\(A\)$$ and the shaded region is bounded by the curve and the lines $$\(x=0\)$$ and $$\(y=0\)$$. Find the exact gradient of the curve at $$\(A\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m20_qp_22 Year：2020 Question No：7(b)
Answer:
Attempt first derivative using chain rule
Obtain \(\frac{\mathrm{d} y}{\mathrm{~d} x}=8 \sin x \cos x+8 \cos x\)
Substitute value from part (a) to find gradient \(-2 \sqrt{3}\)
Obtain \(\frac{\mathrm{d} y}{\mathrm{~d} x}=8 \sin x \cos x+8 \cos x\)
Substitute value from part (a) to find gradient \(-2 \sqrt{3}\)
Knowledge points:
2.4.1 use the derivatives of ,ln x,sin x,cos x,tan x, together with constant multiples, sums, differences and composites
Solution:
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