Math 1 question?

Question

a open top box is constructed from a 4 ft by 6ft rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut.

find the function V that stands for the volume of the box in terms of x

what is the value of x that will produce the maximum volume?

thank you

Answer 1

V=x(6-2x)(4-2x)
V=4x^3-20x^2+24x
dV/dx=12x^2-40x+24
Set to 0 and solve for x
x=2.548 or x=.758
since 2x must be less than 4
x=.758 ft

Answer 2

V(x) = x.(6 - 2x).(4 - 2x)
V(x) = x.(24 - 20x + 4x²)
V(x) = 24 x - 20x² + 4x³
V `(x) = 24 - 40x + 12x² = 0 for Max. volume
3x² - 10x + 6 = 0
x = [10 ± √(100 - 72)] / 6
x = [10 ± √28 ] / 6
x = [10 ± 2√7 ] / 6
x = 5/3 ± √7 / 3
x = (1/3).[5 ± √7]
x = (1/3).[ 5 ± 2.65 ]
x = 2.55 , x = 0.783