Now, to maximize volume, take the derivative and set it equal to zero:
. So, . Check the second derivative: . Since , there is a local maximum at . Hence, the maximum area is given by:
so should be the correct answer.
Then, area is:
Plugging in for , you have:
Then . Setting it equal to zero, you find . The second derivative is always negative, so the area of the window is maximized at that value. So, the maximum area is , so 148 square feet should be the correct answer.