In the rectangular coordinate plane, the graph of the function $f(x)$ defined on the closed interval $[0,5]$ is given in the figure.
If the function $(f \circ f \circ f)(x)$ attains its maximum value at the point $x = a$, in which of the following open intervals is the number $a$?\\
A) $( 0,1 )$\\
B) $( 1,2 )$\\
C) $( 2,3 )$\\
D) $( 3,4 )$\\
E) $( 4,5 )$