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Below is a graph of the function with tangent lines drawn at and . Use the slopes provided in the graph to determine the slope function . Notice that . It might be helpful to make a table of data relating to

The data in the table was taken from the graph.
'' represents -values.
'' represents slope of the tangent line.








The original graph, , is cubic. Does the table of slopes also appear to have a cubic pattern? If not, what type of function would model its pattern?

The slopes have a quadratic pattern! Clearly, the data does not fit the parent quadratic equation: . Find a transformation of that models the data.

Increasing cubic curve, centered at the origin, with 4 tangents, labeled as follows: at the point (negative 2, comma negative 16), m =. 24, at the point (negative 1, comma negative 2), m = 6, at the point (1, comma 2), m = 6, & at the point (2, comma 16),  m = 24.

Use the eTool below to view the tangent lines.
Click on the link to the right to view the full version of the eTool: Slope at a Point eTool