Standard +0.3 This is a straightforward stationary point problem requiring differentiation using the chain rule (for sin 2x and tan 2x), setting the derivative to zero, and solving a trigonometric equation. While it involves composite functions and trig identities, it follows a standard procedure with no novel insight required, making it slightly easier than average.
3
\includegraphics[max width=\textwidth, alt={}, center]{cc7e798e-0817-405c-bae0-b24b9f451fbf-04_378_486_260_826}
The diagram shows the curve with equation
$$y = 5 \sin 2 x - 3 \tan 2 x$$
for values of \(x\) such that \(0 \leqslant x < \frac { 1 } { 4 } \pi\). Find the \(x\)-coordinate of the stationary point \(M\), giving your answer correct to 3 significant figures.
3\\
\includegraphics[max width=\textwidth, alt={}, center]{cc7e798e-0817-405c-bae0-b24b9f451fbf-04_378_486_260_826}
The diagram shows the curve with equation
$$y = 5 \sin 2 x - 3 \tan 2 x$$
for values of $x$ such that $0 \leqslant x < \frac { 1 } { 4 } \pi$. Find the $x$-coordinate of the stationary point $M$, giving your answer correct to 3 significant figures.\\
\hfill \mbox{\textit{CAIE P2 2018 Q3 [5]}}