# Math 3c Derivation - Maximum Volume of Box

English is not my primary language so bear with me as I struggle to translate this.

Jonas is going to make a box without a top which measures 60 cm x 30 cm.

He is going to cut away equally big squares in each corner, and then fold up the sides.

The squares have the sides of x.

Help Jonas to calculate the side x so that the boxes volume gets as big as it can get.

How I tried to solve it:

x(60 - 2x)(30 - 2x)

= (60x - 2x^2)(30 - 2x)

= 1800x - 120x^2 - 60x^2 + 4x^3

y' = 1800 - 240x - 120x - 12x^2

12x^2 - 360x + 1800 = 0

According to PQ :

x1 = 354,92856

x2 = 5,07144

according to the definition x1 is to big

x = 5,07144