Mathematics - Application of Derivative Question with Solution | TestHub

Since Rolle's theorem is satisfied $$\begin{array}{c}\therefore {\mathrm{f}}^{\prime }(\mathrm{c})=0\Rightarrow {\mathrm{e}}^{\mathrm{c}}\sin \mathrm{c}+\cos {\mathrm{e}}^{\mathrm{c}}=0\\ \Rightarrow {\mathrm{e}}^{\mathrm{c}}\{\sin \mathrm{c}+\cos \mathrm{c}\}=0\\ \therefore \mathrm{sinc}+\mathrm{cosc}=0\left(\because {\mathrm{e}}^{\mathrm{c}}\ne 0\right)\\ \Rightarrow \mathrm{tanc}=-1\Rightarrow \mathrm{c}={\tan }^{-1}(-1)=\pi -\frac{\pi }{4}=\frac{3\pi }{4}\end{array}$$