A specialized cooling tank for industrial lasers is being designed in the shape of an open-topped cuboid. The tank is constructed from high-grade sheet metal. The base of the tank has a length of $3 x$ metres and a width of $x$ metres. the vertical height of the tank is $h$ metres.

Given that the volume of the tank must be exactly $m3162\text{ m}^3$ :

Show that the total surface area $m2A\text{ m}^2$ of the metal required is given by

3x^2 + \frac{432}{x}

Use calculus to find the value of $x$ for which $A$ is stationary, giving your answer to 3 significant figures.

Calculate the value of $d2Adx2\frac{d^2A}{dx^2}$ at the stationary point and hence determine whether this value of $x$ minimizes the amount of metal used.

Given that the volume of the tank must be exactly $m3162\text{ m}^3$ :

Show that the total surface area $m2A\text{ m}^2$ of the metal required is given by

3x^2 + \frac{432}{x}

Use calculus to find the value of $x$ for which $A$ is stationary, giving your answer to 3 significant figures.

Calculate the value of $d2Adx2\frac{d^2A}{dx^2}$ at the stationary point and hence determine whether this value of $x$ minimizes the amount of metal used.

1.6 Differentiation

Question 64

Markscheme

1.6 Differentiation

Question 64

Markscheme

1.6 Differentiation

Question 64

1.6 Differentiation Questions

1.6 Differentiation

Question 64

1.6 Differentiation Questions