A rectangle has one corner in first quadrant on the graph of $\"\"$ .

(a) Express the area $\"\"$ of the rectangle as a function of $\"\"$ .

The length of the rectangle is are $\"\"$ and width of the rectangle is $\"\"$ .

Area of the rectangle is $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$ .

(b) Find the domain of $\"\"$ .

Since $\"\"$ is located above $\"\"$ -axis and right to the $\"\"$ -axis, therefore $\"\"$ and $\"\"$ .

Solution of the inequalities $\"\"$ and $\"\"$ .

Include the solution of two inequalities is $\"\"$ .

Domain of $\"\"$ in interval notation : $\"\"$

Domain in set notation $\"\"$ .

(c)

Graph the function $\"\"$ .

Graph of the function $\"\"$ :

$\"\"$

Since $\"\"$ is located above $\"\"$ -axis and right to the $\"\"$ -axis, therefore $\"\"$ .

Locate the relative maximum point on the graph.

$\"\"$

Observe the graph, $\"\"$ is largest when $\"\"$ .

(a) The function is $\"\"$ .

(b) Domain in set notation $\"\"$ .

(c) Graph of the function $\"\"$ :

$\"\"$

The area $\"\"$ is largest when $\"\"$ .