Calculus Lab Write-up Week 6 Derivatives of Powers Type or write your name and the names of the people in your group at the top of 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 Explain: Clearly and thoroughly explain your answers to these questions based on the work you did with your group on labs this week. Where needed, include graphs, tables, diagrams, or screenshots from computer work in programs like Desmos or Geogebra. These questions refer to Lab 5: Derivatives of Powers. (a) (Part 1) Investigate whether the power rule will work when n = . Here are some things to include in your write-up: i. Explain what the exponent , mean and give the domain of the function f(x) = 12. ii. Where is the slope of the function f(x) = x2 increasing and decreasing? iii. Use Desmos to create a graph that also shows whether or not this "rule" works for n = 2. iv. Is the domain of f(x) = 12 the same as the domain of the derivative function f'(x)? Explain why or why not. (b) (Part 2) Remember that the area of a circle with radius r is A(r) = wr2. Find the value of A'(5), and explain using pictures and full sentences what this is telling you about the area of a circle with radius 5. (c) (Part 4) Write the following sentence two different ways using different versions of deriva- tive notation: "The derivative of the function 2 when x = 2 is 192." Explain what you see as the benefits or drawbacks of each of these notations. 2. (10 points) Summarize: What do you think are the big ideas for calculus in the Week 6 Lab? What you want to remember from your work on this lab? Be sure to include definitions or examples of important vocabulary. 3. (10 points) Reflect: Write a short reflection (4-5 sentences or more) on how working on the Week 6 Lab went for you. . 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? . What questions do you still have about the situations or functions in this lab that you would like to discuss more