A sheet of metal that is 30cm wide and 6m long is used to make a rectangular eavestrough by bending the sheet along the dotted lines. what values of x maximizes the capacity of the eavestrough

The volume of the rectangular eavestrough would be:

V = (x) (30 - 2x) (600)

V = (30x - 2x^2) (600)

V = 18000x - 1200x^2

to maximize the capacity of the rectangular eavestrough, get the first derivative and equate it to zero

dV / dx = 18000 - 2400x

equate to zero

18000 - 2400x = 0

2400x = 18000

x = 7.5 cm is the value of x that would maximize its capacity