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9.9 Using Second Derivatives

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Question 10

An aquaculture company is designing a rectangular treatment tank with an open top. The tank is to have a base where the length is exactly twice the width. Let the width of the base be $w$ metres and the height of the tank be $h$ metres.

Given that the capacity of the tank is fixed at $\text{ m}^3$ :

Show that the total internal surface area, $\text{ m}^2$ , of the tank is given by

2w^2 + \frac{864}{w}

[4]

Use algebraic differentiation to find the value of $w$ for which $S$ has a stationary point.

[3]

Justify by further differentiation that this value of $w$ gives a minimum internal surface area for the tank.

[3]

Markscheme

9.9 Using Second Derivatives Questions

A Level
Maths
9.9 Using Second Derivatives

57 exam-style questions on Edexcel A Level Maths 9.9 Using Second Derivatives. Each one has a worked solution and a mark scheme showing where the marks go.

9.9 Using Second Derivatives

Question bank

9.9 Using Second Derivatives

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Question 10

Given that the capacity of the tank is fixed at $\text{ m}^3$ :

Show that the total internal surface area, $\text{ m}^2$ , of the tank is given by

2w^2 + \frac{864}{w}

[4]

Use algebraic differentiation to find the value of $w$ for which $S$ has a stationary point.

[3]

Justify by further differentiation that this value of $w$ gives a minimum internal surface area for the tank.

[3]

Markscheme

9.9 Using Second Derivatives Questions

A Level
Maths
9.9 Using Second Derivatives

57 exam-style questions on Edexcel A Level Maths 9.9 Using Second Derivatives. Each one has a worked solution and a mark scheme showing where the marks go.