If the space-time curve was quantified and has a mathematical function what would the derivative of the function mean? [closed]

Say I have a massive object: This object as we know causes spacetime to bend and curve. The "maximum curve" which I would define as the line in space time that runs directly through the center of the object has the maximum displacement from the space time of zero. This "maximum curve" would take the shape similar to a upside down bell curve or a upside down first derivative of a logistic function:

What would the derivative of the above functions mean? (either the derivative of the bell curve or the second derivative of the logistic function). What would each individual point on the derivative mean: acceleration at that point? Velocity?

I apologize if my wording is poor. I am simply a curious high school student who has completed only the most basic physics and calculus courses. Any help in simplifying my questions or my descriptions would be welcome.

• Your definition of "maximum curve" is ambiguous. Even confined to 3-D space, there are an infinity of curves that pass through any point. Further complicating the issue, in 4-D spacetime, an object's center is no longer a single point but a worldline. Jun 20 '18 at 16:16
• Jun 20 '18 at 17:51
• Ahoy! If you'd like to learn about the math necessary for understanding general relativity I'd highly recommend MathTheBeautiful's tensor calculus series on YouTube! Jun 27 '18 at 22:06