Question

The function f(x)=-(x-3)^2+9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?

A)3 square units
B)6 square units
C)12 square units
D)9 square units

Answer 1

9 square units

Explanation:

Answer 2

D) 9 square units

Explanation:

The squared term will always be non-negative, so the least it can be is zero (for x=3). The squared term is subtracted from 9, so the most the function value can be is 9.

The maximum area of the rectangle is 9 square units.