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9.9 Using Second Derivatives

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Question 22

The power consumption, $w$ (in watts), of a submersible exploration drone at depth $d$ (in meters) is modelled by the equation

3d^3 - 40d + \frac{k}{d}, \quad d > 0

where $k$ is a constant. The drone has a stationary point in its power consumption at depth $P$ where $d = 2$ .

Show that $k = - 16$ .

[3]

Determine the nature of the stationary point at $P$ , justifying your answer.

[3]

The power consumption model suggests there is a second stationary point at a different depth.

Using algebra, find the depth of this second stationary point.

[4]

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 22

The power consumption, $w$ (in watts), of a submersible exploration drone at depth $d$ (in meters) is modelled by the equation

3d^3 - 40d + \frac{k}{d}, \quad d > 0

where $k$ is a constant. The drone has a stationary point in its power consumption at depth $P$ where $d = 2$ .

Show that $k = - 16$ .

[3]

Determine the nature of the stationary point at $P$ , justifying your answer.

[3]

The power consumption model suggests there is a second stationary point at a different depth.

Using algebra, find the depth of this second stationary point.

[4]

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.