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

> Derivatives of Curves. How do they work?

Basically, the slope of a curve at each point.

> How is the second derivative of a quadratic equation a constant?

Well the slope of quadratic curve is increasing at a constant rate.

The quadratic curve is increasing at a quadratic rate (by definition).

But the slope is increasing at a constant rate, which is why the 1st derivative is a straight diagonal line.

So the second derivative is simply the slope of the 1st derivative, which is constant since it is a straight line.