A chemical reaction's rate RRR (measured in units/s) and the concentration CCC of the substrate (measured in mmol/L) are related by the equation
R3+5C2−30RC=0 R^3 + 5C^2 - 30RC = 0 R3+5C2−30RC=0The graph of this relationship for C,R≥0C, R \ge 0C,R≥0 forms a loop in the first quadrant with a stationary point at PPP, where the rate of change of RRR with respect to CCC is zero.
Show that at the point PPP, the rate RRR satisfies the equation
R2(R−45)=0 R^2(R - 45) = 0 R2(R−45)=0Hence, find the coordinates of PPP in the form (C,R)(C, R)(C,R).
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.
