Question: A rectangle is inscribed in the region bounded by the x-axis, the y-axis, and the graph of x + 2y 8 = 0, as shown

A rectangle is inscribed in the region bounded by the x-axis, the y-axis, and the graph of
x + 2y ˆ’ 8 = 0, as shown in the figure.

(a) Write the area A of the rectangle as a function of x.
(b) Determine the domain of the function in the context of the problem.
(c) Construct a table showing possible values of x and the corresponding areas of the rectangle. Use the table to estimate the dimensions that produce the maximum area.
(d) Use a graphing utility to graph the area function. Use the graph to approximate the dimensions that produce the maximum area.
(e) Write the area function in standard form to find analytically the dimensions that produce the maximum area.

y x+ 2y 8 = 0 3 (1, y) 2 3 4 5 6 7 8

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