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Find the dimensions that give the largest area for the rectangle shown in the figure. Its base is on the x-axis and its other two vertices are above the x-axis, lying on the parabola  y = k − x2, k = 8.  (Round your answers to two decimal places.)

Find the dimensions that give the largest area for the rectangle shown in the figure. Its base is on the x-axis and its other two vertices are above the x-axis, lying on the parabola  y = k − x2, k = 8.  (Round your answers to two decimal places.)

Calculus: Early Transcendentals
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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Find the dimensions that give the largest area for the rectangle shown in the figure. Its base is on the x-axis and its other two vertices are above the x-axis, lying on the parabola 

y = k − x2, k = 8.

 (Round your answers to two decimal places.)

The image contains a graph illustrating a downward-opening parabola with the equation \( y = k - x^2 \). The parabola is symmetric about the y-axis. A rectangle is inscribed under the parabola. The rectangle's base lies on the x-axis, and its top side touches the parabola. The vertex of the parabola is at the point where the function achieves its maximum value, \( k \), when \( x = 0 \). The point \( (x, y) \) is marked on the parabola and the rectangle, showing where the top right corner of the rectangle touches the parabola. The x-axis and y-axis are marked with arrows, indicating the positive directions. The origin is marked as \( 0 \). The blue color is used to fill the rectangle for visual clarity.
Transcribed Image Text:The image contains a graph illustrating a downward-opening parabola with the equation \( y = k - x^2 \). The parabola is symmetric about the y-axis. A rectangle is inscribed under the parabola. The rectangle's base lies on the x-axis, and its top side touches the parabola. The vertex of the parabola is at the point where the function achieves its maximum value, \( k \), when \( x = 0 \). The point \( (x, y) \) is marked on the parabola and the rectangle, showing where the top right corner of the rectangle touches the parabola. The x-axis and y-axis are marked with arrows, indicating the positive directions. The origin is marked as \( 0 \). The blue color is used to fill the rectangle for visual clarity.
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