\[ \mathrm{f}(x)=\sin (2 x)+\ln (x) \quad x>0 \] - Show that \(y=\mathrm{f}(x)\) has a stationary point in the interval \([1,1.1]\)

Question

\[
\mathrm{f}(x)=\sin (2 x)+\ln (x) \quad x>0
\]
(a) Show that \(y=\mathrm{f}(x)\) has a stationary point in the interval \([1,1.1]\)
(b) Staring with \(x_{0}=1.05\), apply the Newton-Raphson procedure twice to find an approximation for the \(x\) coordinate of the stationary point in the interval \([1,1.1]\).