The power consumption PPP (in kW) of an industrial extractor fan is modelled by the equation P=13w3−6w+kw,w>0P = \frac{1}{3}w^3 - 6w + \frac{k}{w}, \quad w > 0P=31w3−6w+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.
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 9.9 Using Second Derivatives with exam-style questions for A Level Maths. 57 questions, 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.