Learning Resources

Investigation 11: Graphing a Polynomial Function

Step C

Use the expression you found in Step B to find the critical points. Set the expression equal to zero and solve for x. The answers you get are the x-coordinates of the critical points. Substitute these values back into the given function to find the corresponding y-coordinates.

Remember:

• Critical points are points that you can use to assist you in curve sketching.
• In this particular graph, the critical points are the local maximum and minimum values and are points where the slope is zero.