Question

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

Answer 1

picture?

Answer 2

help

Answer 3

instead of x im going to use the letter b, so it isnt confused with the times symbol
the volume is Length x height x width = Volume

(6) x (b) x (0.3 - 2b) = V

1.8b - 12b^2 = V

the first derivative of V with respect to b is

dV/db = 1.8 - 24b
this is at a maximum (or possibly minimum) when its first derivative is equal to zero

0 = 1.8 - 24b

solving for b

b = 1.8/24 = 0.075m or 7.5 cm

Answer 4

thx