Mathematics - Application of Derivative Question with Solution | TestHub

$\begin{array}{rl}& f^{\prime }(x)=\cos x-x+1\\ & f^{\prime }(x)=-\sin x-1\end{array}$ $\mathrm{f}$ is decreasing $\forall \mathrm{x}\in \mathrm{R}$ $\begin{array}{rl}& \mathrm{f}(\mathrm{x})=0\\ & \mathrm{f}(0)=2,\mathrm{f}(\pi )=-\pi \end{array}$ $\mathrm{f}$ is strictly decreasing in $[0,\pi ]$ and $\mathrm{f}(0).\mathrm{f}(\pi )<0$ $\Rightarrow$ only one solution of $\mathrm{f}(\mathrm{x})=0$ $\mathrm{S}1$ is correct and $\mathrm{S}2$ is incorrect.