NIMCET 2024 Paper

To find maxima or minima, let us differentiate the function.
${\mathit{f}}^{\prime }\left(\mathit{x}\right)=-3{\mathit{x}}^2+6\mathit{x}=0$
$\Rightarrow \mathit{x}=0,2$
At $\mathit{x}=2$, the function is maximum, and its value is 5 . Hence it is bigger than the value of $\cos \mathit{x}$ and ${\mathit{e}}^{-\mathit{x}}$. But the graph of cubic function can achieve even bigger values at negative values of $\mathit{x}$, for example $\mathit{f}\left(-2\right)=21$, hence at $\mathit{x}=2$, the function achieves only the local maxima.