Answer
$a=f,c=f',b=f''$
Work Step by Step
When the graph $b$ intersects the x-axis, at this x-intercepts points, the graph of $a$ have two inflection points and the graph of $c$ has two horizontal tangents.
Also the curve $a$ have a maximum at $x=0$ that corresponds to the $x$ intercept of the graph of $c$.
The value of the curve $b$ at $x=0$ is negative which confirm that the curve $a$ has a maximum a $x=0$.
From this informations, the curve $a=f,c=f',b=f''$
