Question 1: the geometric meaning of the second derivative (1) the speed of the tangent slope change (2) the concavity of the function (for example, the direction of acceleration always points to the concave edge of the trajectory curve). Take the instantaneous acceleration in physics as an example: according to the definition that there is a point that is not constant in acceleration, the expression of acceleration is: a = lim Δ t→ 0 Δ v/Δ t = dv/dt (that is, speed versus time) and because v=dx/dt, there is the second derivative of a=dv/dt=d2x/dt2, that is, the second derivative f' (x) =

Question 2: Does the second derivative have physical significance? Second derivative?

The so-called second derivative is the derivative of the original function. Take the second derivative of the original function.

For example, the derivative of y = x 2 is y=2x, and the derivative of second derivative y=2x is y=2.

Its significance is as follows:

(1) The speed of tangent slope change

(2) the concavity and convexity of the function (for example, the direction of acceleration always points to the concave side of the trajectory curve)

Question 3: The physical meaning of higher-order derivatives ... There is such a saying, but this knowledge should belong to advanced physics, at least in three-dimensional space, even in four-dimensional space or higher, at least in four-dimensional space. My teacher talked about this concept in physics class, but he didn't give any explanation, because this concept belongs to top talents, so there is little relevant information, and some people even doubt whether speed is an official statement.

If you want to know the relevant knowledge, you'd better go to graduate thesis, doctoral thesis or even higher-level thesis to find relevant information.

On the Relationship between Chaos and Agility is a paper by a professor of Jiangxi Normal University.