A Ratio Function's Maximum

Let $a > 0$ and

1. Let $g(a)$ denote the maximum value of $f(x)$ on the interval $[0, 4]$. Find an explicit expression for $g(a)$. 2. Does there exist $a$ such that the graph of $y = f(x)$ on the interval $(0, 4)$ contains two points at which the tangent lines are perpendicular to each other? If so, find the range of such $a$; if not, explain why.