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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
