Derivatives of Curves. How do they work? How is the second derivative of a quadratic equation a constant? Is the second derivative the slope of the slope?

Question

Derivatives of Curves. How do they work? How is the second derivative of a quadratic equation a constant? Is the second derivative the slope of the slope?

In: Mathematics

Answer 1

The derivate of a function is the rate of change of that function (with respect to a variable).

So if the second derivative is constant that means the rate of change of the rate of change is fixed.

As an example, you can think of the function as a constant acceleration. That implies that the velocity (first derivative) is changing linearly which implies that the distant (the function itself) increases quadratically.