Learning Resources

Investigation 10: Graphing the Slope Function

Step E

Remember, you are comparing the graph of the original function with the graph of its derivative. Remember, as well, that a derivative is basically the slope of a curve. If you are still having difficulty finding connections between the two graphs, perhaps answering the following questions will steer you in the right direction.

Look at the graph of the original function. 

• For what value of x is the function a minimum? 
• If a tangent line that was drawn exactly at the vertex, what type of line would be created? 
• What would be the slope of this tangent line?
• Look at the graph of the slope function. What zero(s) exist?
• Do you see a connection between the x-intercept of the slope function and the x-coordinate of the vertex of the original function?