Below is the graph of a third degree polynomial. We are going to start thinking about what a derivative is by using this graph.

1) Place a point on the graph anywhere you want. Take the point and construct the line through this point that is tangent to the graph of the polynomial. Then calculate it's slope.
2) Repeat step 1 using four different points of your choosing.
3) The derivative of the given function is f'(x)=3x² + 10x +3. Plug the x-values of the points you chose previously into the derivative function. Do you get the same results as when you found the slope of the tangent line? (You should! This is what the derivative does!)