A：$f\left(0\right)<e^{1}f\left(1\right)<e^{2}f\left(2\right)$

B：$e^{2}f\left(2\right)<f\left(0\right)<e^{1}f\left(1\right)$

C：$e^{2}f\left(2\right)<e^{1}f\left(1\right)<f\left(0\right)$

D：$e^{1}f\left(1\right)<f\left(0\right)<e^{2}f\left(2\right)$