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Differentiation

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Question 567

The power consumption PPP (in kW) of an industrial extractor fan is modelled by the equation

P=13w3−6w+kw,w>0 P = \frac{1}{3}w^3 - 6w + \frac{k}{w}, \quad w > 0 P=31​w3−6w+wk​,w>0

where www is the angular velocity in rad/s and kkk is a constant. The fan is observed to have a stationary point in its power profile when w=2w = 2w=2.

a.

Show that k=−8k = -8k=−8.

[3]
b.

Determine the nature of the stationary point when w=2w = 2w=2, justifying your answer.

[3]
c.

The power profile has a second stationary point.

Using algebra, find the exact value of the angular velocity www at this second stationary point.

[3]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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