1.9.17 Concavity and the second derivative (A-level only)

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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]

1.9.17 Concavity and the second derivative (A-level only) Questions

A Level
Maths
1.9.17 Concavity and the second derivative (A-level only)

A Level
Maths OCR (MEI)
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