A sheet of cardboard 12 inches square is used to make an open box by cutting out squares of equal size from the four corners and bending up the sides. What size should the squares be to obtain a box with the largest possible volume

is the size of the square

Step-by-step explanation:

Let the side of the square cut from the cardboard be “x”

Size of the square base = , height of the box = x

Volume of square box = Area * height =

Differentiating the above equation and equating it to zero, we get –  

d/dx

d/dx= d/dx

d/dx

On solving above equation, we get –  

c

step-by-step explanation:

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)