The diagram shows part of the curve with equation $$\(y=x^{3} \cos 2 x\)$$. The curve has a maximum at the point $$\(M\)$$. Show that the $$\(x\)$$-coordinate of $$\(M\)$$ satisfies the equation $$\(x=\sqrt[3]{1.5 x^{2} \cot 2 x}\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_21 Year：2020 Question No：5(a)
Answer:
Differentiate using the product rule to obtain \(a x^{2} \cos 2 x-b x^{3} \sin 2 x\)
Obtain \(3 x^{2} \cos 2 x-2 x^{3} \sin 2 x\)
Equate first derivative to zero and confirm \(x=\sqrt[3]{1.5 x^{2} \cot 2 x}\) AG
Obtain \(3 x^{2} \cos 2 x-2 x^{3} \sin 2 x\)
Equate first derivative to zero and confirm \(x=\sqrt[3]{1.5 x^{2} \cot 2 x}\) AG
Knowledge points:
2.3.2.1 more contents
2.3.2.2 the expansions of
2.3.2.3 the formulae for sin 2A,cos 2A and tan 2A
2.3.2.4 the expression of
2.4.2 differentiate products and quotients
Solution:
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