The function ${\text{⨍ (x)=e}}^{\mathrm{x}+1}\left(4{\mathrm{x}}^2-16\mathrm{x}+11\right)$ is

$$\begin{gathered} f\left(x\right)=e^{x+1}(4x^{2^{ }}-16x+11) \\ f\text{'}\left(x\right)=e^{x+1}(8x-16)+e^{x+1}(4x^2-16x+11)=e^{x+1}(4x^2-8x-5) \\ f\left(x\right) is increa\sin g \Rightarrow f\text{'}\left(x\right)>0 \\ {e}^{x+1}(4x^2-10x+2x-5)>0 \\ 2x(2x-5)+(2x-5)>0 \\ (2x+1)(2x-5)>0 \\ x\in \left(-\infty ,\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)\cup \left(\frac{5}{2},\infty \right) \end{gathered}$$