What is the dimension of the box

Question

An open box is to be made from a 16 𝑐𝑚. by 30 𝑐𝑚. piece of cardboard by cutting out squares of equal size from the corners and bending up the sides. What will be the dimension of the box with the largest volume and the capacity of the box?

Answer 1

V= (16-2x)(30-2x) x= (480 -92x + 4x^2)x = 4x^3 -92x^2 +480x

take the derivative and set it equal to zero

V' = 12x^2 -184x + 480 = 0

3x^2 -46x +120 = 0

x= 46/6 + or - (1/6)sqr(46^2-1440) = 46/6 - 26/6= 20/6 = 3 1/3 cm

dimensions are 16-2x by 30-2x

= 16-6 2/3 by 30 - 6 2/3

= 9 1/3 by 23 1/3 cm