Consider the function $f(x) = x^2 - 3x$. The number

The graph of the traces of point

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*m*is the slope of line*a*tangent to*f*at Point*A*. Point*B*is the ordered pair (*n*,*m*) where*n*is the*x*coordinate of A and m the slope of line*a*. Now drag point*A*along the graph. What do you observe? What can you say about the traces of point B?The graph of the traces of point

*B*is the derivative function of*f*. Can you explain why?Download Applet

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