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# 2. By hand, determine the exact dimensions that maximize the area of the rectangle and state the maximum area. Your work should be shown in

2. By hand, determine the exact dimensions that maximize the area of the rectangle and state the maximum area. Your work should be shown in an organized manner that follows the full step-by-step procedure outlined in video lecture. Does this result confirm your answer to part 1? Include units. (Hint: Keep in mind that the length of the base of the rectangle is double the value of the x-coordinate.) Conclusion: What did you learn from this Tech Lab? Do you feel it gave you a better grasp on the concepts in this module? Is there anything you're still not quite sure about? Page 4 of 4Week 1 Tech Lab: Optimization Rectangle Inscribed Under a Curve Before beginning this lab, be sure to fully read the instructions provided in DIL. Name: Instructions: Consider a rectangle inscribed below the curve f(x) =25 -x and above the x-axis. This rectangle has its base along the x-axis and its two other vertices lie on the curve f(x) =25-x]. Let the units along the axes be in inches. Use the following GeoGebra applet to visualize this rectangle and to answer the questions below. https://www.geogebra.org/classic/m96RqRxu Using the GeoGebra applet, move the point along the curve to see how the rectangle changes, including how its area and perimeter change. Now answer the following: Part A: Maximizing Perimeter 1. Using the GeoGebra applet, guess the rectangle that has maximal perimeter. As a full sentence or paragraph, state the coordinate point that creates the optimum rectangle, the dimensions of the optimum rectangle, and the perimeter of the optimum rectangle. Include units. Page 1 of 42. By hand, determine the dimensions that maximize the perimeter of the rectangle and state the maximum perimeter. Your work should be shown in an organized manner that follows the full step-by-step procedure outlined in video lecture. Does this result confirm your answer to part 1? Include units. (Hint: Keep in mind that the length of the base of the rectangle is double the value of the x-coordinate.) Page 2 of 4Part B: Maximizing Area 1. Using the GeoGebra applet, guess the rectangle that has maximal area. As a full sentence or paragraph, state the coordinate point that creates the optimum rectangle, the dimensions of the optimum rectangle, and the area of the optimum rectangle. Include units. Page 3 of 4

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