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9.9 Using Second Derivatives

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Question 13

A precision-engineered storage vault for high-density alloys is in the shape of a cuboid with a rectangular base of width $x$ cm and length $3 x$ cm. The height of the vault is $h$ cm.

The volume of the vault is fixed at $cm31350\text{ cm}^3$ .

Show that the surface area of the vault, $cm2S\text{ cm}^2$ , is given by

6x^2 + \frac{3600}{x}

[4]

Find $dSdx\frac{dS}{dx}$ .

[2]

Hence find the value of $x$ for which $S$ is stationary, giving your answer to 3 significant figures.

[3]

Find $d2Sdx2\frac{d^2S}{dx^2}$ and hence show that the value of $x$ found in part (c) gives the minimum value of $S$ .

[3]

Hence find the minimum surface area of the vault, giving your answer to 1 decimal place.

[2]

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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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Question 13

A precision-engineered storage vault for high-density alloys is in the shape of a cuboid with a rectangular base of width $x$ cm and length $3 x$ cm. The height of the vault is $h$ cm.

The volume of the vault is fixed at $cm31350\text{ cm}^3$ .

Show that the surface area of the vault, $cm2S\text{ cm}^2$ , is given by

6x^2 + \frac{3600}{x}

[4]

Find $dSdx\frac{dS}{dx}$ .

[2]

Hence find the value of $x$ for which $S$ is stationary, giving your answer to 3 significant figures.

[3]

Find $d2Sdx2\frac{d^2S}{dx^2}$ and hence show that the value of $x$ found in part (c) gives the minimum value of $S$ .

[3]

Hence find the minimum surface area of the vault, giving your answer to 1 decimal place.

[2]

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.