Mathematics - Application of Derivative Question with Solution | TestHub

$f(x)=\frac{\left(x^{2023}+2024x+2025\right)}{e^{\pi x}\left(x^2-x+3\right)}(\sin x+2)$ $\because (\sin x+2)$ is never zero $\therefore$ for $x^{2023}+2024x+2025=0$ $\begin{array}{rl}& \text{ let }\varphi (\mathrm{x})={\mathrm{x}}^{2023}+2024\mathrm{x}+2025\\ & {\varphi }^{\prime }(\mathrm{x})=2023{\mathrm{x}}^{2022}+2024>0\forall \mathrm{x}\in \mathrm{R}\end{array}$ $\therefore \varphi (\mathrm{x})$ is an Strictly Increasing function $\therefore \varphi (\mathrm{x})=0$ for exactly one value of $\mathrm{x}$ $\therefore \mathrm{f}(\mathrm{x})=0$ has one solution