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. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, 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.
