  However, there are more troublesome special cases. Suppose that the car’s position function is given by: \(f(t)=0\) for all \(t \lt 0\), else \(f(t)=t\). Then speed is zero for all \(t \lt 0\), and speed is 1 for all \(t \gt 0\). But what of \(t = 0\)? One should avoid “arbitrary” solutions, which attribute one speed rather than another, but do not give a reason for so privileging. There is of course at least one simple solution that is non-arbitrary, namely that it is neither in motion nor motionless, since its speed is indeterminate at \(t = 0\).  This solution derives from the fact that according to classical calculus there is no derivative of such a function at \(t = 0\).