The largest value of ${\text{f(x)=2x}}^3{\text{-3x}}^2\text{-12x+5}$ for $-2\le \mathrm{x}\le 4$ occurs at $\mathrm{x}=$

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)=2{\mathrm{x}}^3-3{\mathrm{x}}^2-12\mathrm{x}+5 \\ -2\le \mathrm{x}\le 4 \\ {\mathrm{f}}^{\mathrm{I}}\left(\mathrm{x}\right)=6{\mathrm{x}}^2-6\mathrm{x}-12 \end{gathered}$$

$\mathrm{f}\left(\mathrm{x}\right)$ is minimum or maximum

$$\begin{gathered} \Rightarrow {\mathrm{f}}^{\mathrm{I}}\left(\mathrm{x}\right)=0 \\ 6{\mathrm{x}}^2-6\mathrm{x}-12=0 \\ {\mathrm{x}}^2-\mathrm{x}-2=0 \\ \left(\mathrm{x}-2\right)\left(\mathrm{x}+1\right)=0 \\ \mathrm{x}=-1,2 \end{gathered}$$

$$\begin{gathered} \mathrm{f}\left(-2\right)=-16-12+24+5=1 \\ \mathrm{f}\left(-1\right)=16-12-24+5=-15 \\ \mathrm{f}\left(4\right)=128-48-48+5=37 \\ \max \mathrm{at} \mathrm{x}=4 \end{gathered}$$