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9.9 Using Second Derivatives

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Question 39

The profit $P$ , in thousands of pounds, generated by a chemical plant is modeled by the equation

54v^{\frac{1}{2}} - 2v^{\frac{3}{2}} + 10, \quad v > 0

where $v\,$ is the volume of a specific catalyst used in litres.

Find $dPdv\dfrac{dP}{dv}$ , giving each term in its simplest form.

[2]

Hence find the coordinates of the stationary point of the profit model.

[3]

Find $d2Pdv2\dfrac{d^2 P}{dv^2}$ and hence determine the nature of this stationary point.

[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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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 39

The profit $P$ , in thousands of pounds, generated by a chemical plant is modeled by the equation

54v^{\frac{1}{2}} - 2v^{\frac{3}{2}} + 10, \quad v > 0

where $v\,$ is the volume of a specific catalyst used in litres.

Find $dPdv\dfrac{dP}{dv}$ , giving each term in its simplest form.

[2]

Hence find the coordinates of the stationary point of the profit model.

[3]

Find $d2Pdv2\dfrac{d^2 P}{dv^2}$ and hence determine the nature of this stationary point.

[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.