Question

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

Answer 1

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