The profit PPP, in thousands of pounds, generated by a chemical plant is modeled by the equation
P=54v12−2v32+10,v>0 P = 54v^{\frac{1}{2}} - 2v^{\frac{3}{2}} + 10, \quad v > 0 P=54v21−2v23+10,v>0where 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 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.
