A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow.

A. 5 inches

B. 4 inches

C. 4.5 inches

D. 5.5 inches

The sides can be divided into (whre x is height and y is bottom)

2x+y=18

max area is xy

solve for x which is height

2x+y=18

minus 2x both sides

y=18-2x

sub that for y

xy=max

x (18-2x) = max

-2x^2+18x=max

to find teh x value of the vertex, when

ax^2+bx+c=0

xvalue of vertex is - b/2a

-18 / (2*-2) = - 18/-4=9/2=4.5

answer is 4.5in

C is answer