1.50: Past-paper question 7

Figure 3 shows a solid cuboid with sides of length $\displaystyle x$ cm, $\displaystyle 2x$ cm and $\displaystyle y$ cm

The volume of the cuboid is $\displaystyle 72 \mathrm{cm}^3$

The total surface area of the cuboid is $\displaystyle A$$\displaystyle \mathrm{cm}^2$

(a) Show that $\displaystyle A = \frac{216}{x} + 4x^2$

(b) Use calculus to find the minimum value of $\displaystyle A$
Justify that your value is a minimum value of $\displaystyle A$