Small slope approximation: what can you say about curvature and higher derivatives?

[hanson]

Hi all, if you have a small slope approcimation, what can you say about the curvature? and higher derivatives of the slope?

 

[HallsofIvy]

You aren't getting any responses to this. It might help if you would explain what you mean by "small slope approximation". Approximation to what?

 

[hanson]

You aren't getting any responses to this. It might help if you would explain what you mean by "small slope approximation". Approximation to what?

Thanks for helping me. By small slope approximation, I mean the slope dy/dx is assumed to be small.

The confusion I am having now is: If we assume dy/dx to be small, can we say anything about d^2y/dx^2? or y itself?

Can I say that dy/dx is of order (y/x), d^2y/dx is of order (y/x^2) and etc.?