The diagram shows part of the curve with equation $$$y=x^{3} \cos 2 x$$$. The curve has a maximum at the point $$$M$$$. Use the equation in part (a) to show by calculation that the $$$x$$$-coordinate of $$$M$$$ lies between $$$0.59$$$and $$$0.60$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_21 Year：2020 Question No：5(b)

Answer:

Consider sign of $x-\sqrt[3]{1.5 x^{2} \cot 2 x}$ or equivalent for $0.59$ and $0.60$
Obtain $-0.009 \ldots$ and $0.005 \ldots$ or equivalents and justify conclusion

Knowledge points:

2.6.1 locate approximately a root of an equation, by means of graphical considerations and/or searching for a sign change

Answer:

Knowledge points:

Solution:

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