Related Rates Walkthrough Name _________________________ Period ________________________ Directions: Read each problem below and complete the subsequent numbered task. Show significant work for each step. Use the applet to verify the solution. A 10 meter ladder is leaning against the vertical wall. If the base of the ladder is pulled horizontally away from the house at a rate of 0.6 meters per second, how fast is the top of the ladder sliding down that wall at the instant when the base of the ladder is 4 meters from the wall?  Identify the geometric shape and determine variables. Shape ________________________ Variables _________________________  Will the length of the ladder change as it slides down the wall? ____________  Write the variables rates of change as derivatives with respect to time. Note which ones are known and which one is needed to be found. *4+ Determine the relationship between the variables (hence “related rate”). Write the proper geometric formula here.  Differentiate the geometric formula implicitly with respect to time.  Plug in known values and solve. Teacher Resources Standards: Calculus AB II. Derivatives, Application of Derivatives: Modeling rates of change, including related rates problems. Objectives: Students will setup and solve related rates problems Students will apply prerequisite knowledge of geometry to related rates Students will apply previously learned implicit differentiation Materials: Computer Lab Accessibility to GeoGebra through installed software or Internet (webstart) Ladder Sliding Down Wall interactive Geogebra file Related Rates Walkthrough Worksheet Notes: Confirm that the file works in the lab on student computer before class Distribute worksheets and individually guide students as needed Global questions: Why is the answer for dwall negative? What additional calculation needs to be made to solve for dwall? (Pythagorean Theorem is needed to solve for wall) Extension: Give each student a different set of values to solve for dwall. Students will be able to verify each answer with GeoGebra.