1.38: Open cuboid with minimum surface area

0606/12/M/J/19 — Question 10 · 9 marks

1.38 diagram
The diagram shows an open container in the shape of a cuboid of width xx cm, length 4x4x cm and height hh cm. The volume of the container is 800800 cm3^3.
(i)
Show that the external surface area, SS cm2^2, of the open container is such that S=4x2+2000xS = 4x^{2} + \dfrac{2000}{x}.
[4]
(ii)
Given that xx can vary, find the stationary value of SS and determine its nature.
[5]