What is the definition of the second derivative?

[TI]

I know the first derivative means the slope of the tangent.  What does the second one mean? Third?

[federox]

The second derivative is the derivative of the derivative: the rate of change of the rate of change.

The third derivative is the derivative of the derivative of the derivative: the rate of change of the rate of change of the rate of change.

Have a good day!

[Hawke]

The second derivative gives you concavity; it tells you, at a given point, whether the curve is concave up or concave down.