With a Tangent to the curve in point A, we can find the Instantaneous rate of change (IRC) of the curve in A. We find the IRC by calculating the slope of the tangent. The IRC will vary as we move A along the curve.
Furthermore, there is a function that calculates the IRC (hence slope of the tangent) in any point A. That function is called the derivative. Because the derivative is a function, we can graph it on the same set of axes.
The derivative tells us where the original function is increasing or decreasing.
We can even find the derivative of the derivative (the second derivative) and graph it. what will this tell us...?