Week 10 Implicit Differentiation Include your name and the names of the people in your group on your lab write-up. Each person will submit their own lab write-up, saved as a PDF to the online system. 1. (80 points) Demonstrate and Explains Clearly and thoroughly explain your answers to these questions based on the work you did with your group on labs this week. These questions refer to Lab 10A: Implicit Differentiation. (a) (From Lab JOB) i. (Part ?) Consider the equation a' + y' = 45ry. A. Show and explain how to find the derivative of both sides of this equation. Be sure to explain where comes from. B. Use the derivative equation to find the slope of the tangent line to this curve at the point (2, 1) and write an equation for this tangent line. C. Graph s' + y = 4 5ry and this tangent line on the same axes and show that they are tangent at the point (2, 1). li. (Part 3) Consider the circle a? + y' = 169. Show that the point (5,12) is on this circle and find the equation for line tangent to the circle through the point (5, 12). (b) (10 points) Summarize: What do you think are the big ideas for calculus in the 10A and 10B? What you want to remember from your work on these labs? Be sure to include definitions or examples of important vocabulary related to optimization and the use of the derivative function in this context. (c) (10 points) Reflect: Write a short reflection (4-5 sentences or more) on how working on the week 10 labs went for you. . What questions do you still have about optimization using derivatives that you would like to discuss more? . What worked well in collaborating with the members of your group? What could have gone better? . What could you try doing for the next lab to improve your learning