Express rectangle area as function of x

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SUMMARY

The area A of a rectangle defined by the graph of y=36-x^2, the origin, and the axes can be expressed as a function of x. The base of the rectangle is represented by x, while the height is given by the function y=36-x^2. Therefore, the area A can be formulated as A(x) = x(36-x^2). The domain of A is [0, 6], and the maximum area occurs at x=3, yielding an area of 54 square units.

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kbillsy
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Hey so another expressing functions question:

A rectangle has on corner on the graph of y=36-x^2, another at the origin, a 3rd on the positive y-axis, and the fourth on the positive x-axis. Express the area A of the rectangle as a function of x. What is the domain of A? For what value of x is A largest?
 
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Let's look at a diagram:

View attachment 2132

In terms of $x$, what is the base of the rectangle...what is its height?
 

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