Final answer:
The maximum area of a rectangle with a perimeter of 12 units is achieved by forming a square, with each side measuring 3 units. Hence, the maximum area is 3 units by 3 units, which equals 9 square units.
Step-by-step explanation:
The maximum area of a rectangle with a perimeter of 12 units, as described by the function f(x) = -3x + 9, can be determined by considering the rectangular shape where the length and width are related to the perimeter. The perimeter (P) of a rectangle is given by P = 2l + 2w (where l is length and w is width). Given that the perimeter is 12 units, we can express one dimension in terms of the other and substitute it into the area formula A = l × w. However, to maximize the area of the rectangle, a square is the best option since a square is a special case of a rectangle where all sides are equal, maximizing the enclosed area.
For a square, each side would be P/4, which is 12/4 = 3 units. Therefore, the area of the square (which is also the maximum area that can be achieved within the given constraints) is 3 units × 3 units = 9 square units.
Therefore, the correct answer is c) 9 square units.