The power consumption, www (in watts), of a submersible exploration drone at depth ddd (in meters) is modelled by the equation w=3d3−40d+kd,d>0w = 3d^3 - 40d + \frac{k}{d}, \quad d > 0w=3d3−40d+dk,d>0 where kkk is a constant. The drone has a stationary point in its power consumption at depth PPP where d=2d = 2d=2.
Show that k=−16k = -16k=−16.
Determine the nature of the stationary point at PPP, justifying your answer.
The power consumption model suggests there is a second stationary point at a different depth.
Using algebra, find the depth of 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.