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3-11.

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 . Homework Help ✎

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

  

  

 

m

 

 

 

  

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.

graph at right

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