# The...er...derivendicular

**Calculus**Level pending

In this problem, two functions are defined to be **perpendicular at all x in their domain** if for every x in their domain, the tangent lines of those functions at x are perpendicular.

A function \( f(x) \) defined on \( x \leq 0 \), is perpendicular at all x in their domain to the function \( f'(x) \).

If \(f(0) = 0\), what is \(f(-4.5)\))?