Mathematics - Application of Derivative Question with Solution | TestHub

\begin{array}{l} \text { Given, } f(x)=x^{3}+3 x-2 \\ \Rightarrow f^{\prime}(x)=3 x^{2}+3 \\ \text { Put } f^{\prime}(x)=0 \Rightarrow 3 x^{2}+3=0 \\ \Rightarrow x^{2}=-1 \end{array} $\Rightarrow x^2=-1$ $\therefore f(x)$ is either increasing or decreasing At $x=2,f(2)=2^3+3(2)-2=12$ At $x=3,f(3)=3^3+3(3)-2=34$ $\therefore f(x)\in [12,34]$