(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 .