The profit PPP, in thousands of pounds, generated by a chemical plant is modeled by the equation
P=54v12−2v32+10,v>0P = 54v^{\frac{1}{2}} - 2v^{\frac{3}{2}} + 10, \quad v > 0P=54v21−2v23+10,v>0
where v v\,v is the volume of a specific catalyst used in litres.
Find dPdv\dfrac{dP}{dv}dvdP, giving each term in its simplest form.
Hence find the coordinates of the stationary point of the profit model.
Find d2Pdv2\dfrac{d^2 P}{dv^2}dv2d2P and hence determine the nature of this 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.