Show that the function f given by $\displaystyle \mathrm{f}(x)=\sin x+\cos x$, is strictly decreasing in the interval $\displaystyle \left(\frac{\pi}{4}, \frac{5 \pi}{4}\right)$.

$$\begin{aligned} & \mathrm{f}(x)=\sin x+\cos x \Rightarrow \mathrm{f}^{\prime}(x)=\cos x-\sin x \\ & \mathrm{f}^{\prime}(x)=0 \Rightarrow x=\frac{\pi}{4}, \frac{5 \pi}{4} \text { Thus,in the interval }\left(\frac{\pi}{4}, \frac{5 \pi}{4}\right) \mathrm{f}^{\prime}(x)<0 \\ & \therefore \mathrm{f} \text { is strictly decreasing function on }\left(\frac{\pi}{4}, \frac{5 \pi}{4}\right) \end{aligned} $$