### Home > APCALC > Chapter 3 > Lesson 3.1.1 > Problem 3-11

Below is a graph of the function with tangent lines drawn at

*and*

*. 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.*

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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.*

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*