jmc

If the graph of $f$ can be drawn without lifting your pencil from the paper, then the graphs of the two cases must meet when $x=a$, which (loosely speaking) is the dividing point between the two cases. Therefore, we must have $$\begin{array}{rl}5a^2+2& =11a\\ \Rightarrow 5a^2-11a+2& =0\\ \Rightarrow (-5a+1)(-a+2)& =0.\end{array}$$Solving this equation gives $a=\frac{1}{5}$ or $a=2$. The smaller value is $\boxed{\frac{1}{5}}$.