\[\boxed{\mathbf{2.437}}\]
\[x = 1 \rightarrow \frac{4}{7} \cdot 1 = \frac{4}{7}\]
\[x = \frac{1}{8} \rightarrow \frac{4}{7} \cdot \frac{1}{8} = \frac{4}{56} = \frac{1}{14}\]
\[x = 1\frac{3}{4} = \frac{7}{4} \rightarrow \frac{4}{7} \cdot \frac{7}{4} = 1\]
\[x = \frac{3}{8} \rightarrow \frac{4}{7} \cdot \frac{3}{8} = \frac{12}{56} = \frac{3}{14}\]
\[Наибольшее\ значение:1.\]
\[Наименьшее\ значение:\ \frac{1}{14}.\]