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=31w3−6w+wk,w>0where 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.
Show that k=−8k = -8k=−8.
Determine the nature of the stationary point when w=2w = 2w=2, justifying your answer.
The power profile has a second stationary point.
Using algebra, find the exact value of the angular velocity www at this second stationary point.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
