Lab 4 -- Exercises to Submit When you're done working through the exercises, edit carefully so only the relevant work remains, and write clear explanations. A sample solution is provided via the Lab 4 folder on BlackBoard. You will submit this lab electronically: in BlackBoard, use the Digital Dropbox found under Course Tools. Be sure to "send" the lab, not just "add" it. For timely submission send your lab no later than the beginning of your class on Tuesday, Oct. 24. (Name the lab with both partner's last names.) Part A For each function, a) Use the first derivative to determine the intervals on which the function is increasing and the intervals on which the function is decreasing. Spell out your conclusions together with an explanation of the work that supports them. b) Use the second derivative to determine the intervals on which the function lies above its tangent lines and the intervals on which the function lies below its tangent lines. Spell out your conclusions together with an explanation of the work that supports them. (Suggestion: examine the graph of the function along with the graphs of both derivatives to verify your answers to a) and b).) (You may use decimal approximations to specify your intervals.) #1. 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(Hint: make sure you find all roots of each derivative in 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 Part B #3. Explore at least two ways to address the problem below. Explain what you did and why it's logically valid for each method. Strive for accuracy. Give your best idea of the range of f(x)= 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. #4. Follow the directions for #3, on the function 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. In at least one of your ways, give exact values (not approximations).