The diagram shows the curve with equation $$$y=\frac{3 x+2}{\ln x}$$$. The curve has a minimum point $$$M$$$. Use the equation in part (a) to show by calculation that the $$$x$$$-coordinate of $$$M$$$ lies between 3 and 4. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_21 Year：2021 Question No：5(b)

Answer:

Consider $x-\frac{3 x+2}{3 \ln x}$ or equivalent for values 3 and 4
Obtain $-0.33 \ldots$ and $0.63 \ldots$ or equivalents and justify conclusion

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