Suppose you have two functions f(x) and g(x) and, whenever the tangent line to f(x) and the tangent line to g(x) are at the same x, those two tangent lines never cross. What can I say about f ´(x) and g´(x)?

Suppose you have two functions f(x) and g(x) and, whenever the tangent line to f(x) and the tangent line to g(x) are at the same x, those two tangent lines never cross. What can I say about f ´(x) and g´(x)?

If the two tangent lines never cross, then by definition they are parallel. Thus f'(x) and g'(x) are the same.