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1.10 G: Differentiation

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Question 211

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

P=54v12−2v32+10,v>0 P = 54v^{\frac{1}{2}} - 2v^{\frac{3}{2}} + 10, \quad v > 0 P=54v21​−2v23​+10,v>0

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

a.

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

[2]
b.

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

[3]
c.

Find d2Pdv2\dfrac{d^2 P}{dv^2}dv2d2P​ and hence determine the nature of this stationary point.

[3]
Markscheme

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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