**(a)** Express the area of the rectangle as a function of .

Since the point is located on the circle , the length of the rectangle is are and width of the rectangle is .

Formula for the area of the rectangle is , where is the length and is the width of the rectangle.

Substitute in .

.

**(b)** Express the perimeter of the rectangle as a function of .

The length of the rectangle is are and width of the rectangle is .

Formula for the perimeter of the rectangle is .

.

**(c)** Graph the function .

Graph of the function :

Locate the maximum point on the graph.

Observe the graph, is largest when .

**(d)** Graph the function .

Graph of the function :

Locate the maximum point on the graph.

Observe the graph, is largest when .

**(a)** The function is

**(b)** The function is .

**(c)** Graph of the function :

is largest when .

**(d)** Graph of the function :

is largest when .

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