3. Given the equation of the semicircle y = v36 – x² . a. Construct a graph of the semicircle and label (x, y) at some point on the semicircle. b. Explain why A = 2xy is the area of the rectangle under the semicircle and above the X-axis that includes the point (x, y). C. Construct a function f (x) that represents the area of the inscribed rectangle. d. Construct a graph of that function. e. Use the maximum finder on the graphing calculator to identify the local maximum. f. Determine the point (x, y) that results in the rectangle with the largest area. Round the coordinates to two decimal places. g. Determine the area of the largest possible rectangle. - %3D
3. Given the equation of the semicircle y = v36 – x² . a. Construct a graph of the semicircle and label (x, y) at some point on the semicircle. b. Explain why A = 2xy is the area of the rectangle under the semicircle and above the X-axis that includes the point (x, y). C. Construct a function f (x) that represents the area of the inscribed rectangle. d. Construct a graph of that function. e. Use the maximum finder on the graphing calculator to identify the local maximum. f. Determine the point (x, y) that results in the rectangle with the largest area. Round the coordinates to two decimal places. g. Determine the area of the largest possible rectangle. - %3D
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:3. Given the equation of the semicircle y = v36 – x² .
a. Construct a graph of the semicircle and label (x, y) at some point on the semicircle.
b. Explain why A = 2xy is the area of the rectangle under the semicircle and above the
X-axis that includes the point (x, y).
C. Construct a function f (x) that represents the area of the inscribed rectangle.
d. Construct a graph of that function.
e. Use the maximum finder on the graphing calculator to identify the local maximum.
f. Determine the point (x, y) that results in the rectangle with the largest area. Round
the coordinates to two decimal places.
g. Determine the area of the largest possible rectangle.
-
%3D
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