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