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 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.
