A cuboid has width 2x 2x\,2x cm, height x x\,x cm and depth y y\,y cm.
The volume of the cuboid is 600 cm3^33, and its surface area is S S\,S cm2^22.
Show that S=4x2+1800xS = 4x^2 + \dfrac{1800}{x}S=4x2+x1800.
Determine the value of x x\,x for which the surface area of the cuboid is a minimum, giving your answer to 3 significant figures.
Find, to the nearest integer, the minimum value of SSS.
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.