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

Below is the graph of the function

*f*(*x*) = 2*x*^{3}with tangents drawn at*x*= −2, −1, 1, and 2. Use the slopes provided in the graph to find the slope function*f*′(*x*). Notice that*f*′(0) = 0. It might be helpful to make a table of data relating*x*to*m*. Homework Help ✎

The data in the table was taken from the graph.

'*x*' represents *x*-values.

'*m* ' represents slope of the tangent line.

The original graph, *f*(*x*), 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: *y* = *x*^{2}. Find a transformation of *y* = *x*^{2} 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