If $$f'(x)$$ and $$g'(x)$$ exist for all $$x \in R$$, and if $$f'(x)>g'(x)$$ for all $$x \in R$$, then the curve $$y = f(x)$$ and $$y = g(x)$$ in the $$xy$$-plane

Let, $$h(x)=f(x)-g(x).$$

Then, $$h'(x)=f'(x)-g'(x)$$

Now according to question, $$f'(x)>g'\left(x\right)$$

So, $$f'(x)-g'\left(x\right)>0$$

So, $$h'(x)>0$$
So, h(x) is an increasing function.

Hence, there are two cases possible:-

Case 1:- The curve lies only in positive y axis. In this case it won't intersect x-axis. So, number of points of intersection is zero.

Case 2:- The curve is moving from negative y axis to positive y axis, since it is increasing. In this case it will intersect x-axis at 1 point. So, number of points of intersection is 1.

So option B.