Tuesday, May 3, 2011

Tracing the Derivative

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

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The graph of the traces of point B is the derivative function of f. Can you explain why?

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