I'm pretty convinced but I need to make sure I'm right about this.
By a sharp edge, I mean a point in the graph where the curve is not differentiable.
in motion graphs, (x,y,z) coordinates depend on t polynomially.
All quantities in motion depend on coordinates and t.
Since operations on differentiable functions result in a differentiable function, motion graphs cannot have sharp edges (points where the curve cannot be differentiated)
Is this right?