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