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1.7 Differentiation

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Question 254

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=0

The 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.

a.

Show that at the point PPP, the rate RRR satisfies the equation

R2(R−45)=0 R^2(R - 45) = 0 R2(R−45)=0
[5]
b.

Hence, find the coordinates of PPP in the form (C,R)(C, R)(C,R).

[3]
Markscheme

1.7 Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.7 Differentiation

425 exam-style questions on OCR A Level Maths 1.7 Differentiation, covering 1.7.1 Derivative as gradient of the tangent, 1.7.2 Gradient of the tangent at a point, 1.7.3 Sketching the gradient function, 1.7.4 Second derivatives, 1.7.5 Second derivative as rate of change of gradient, 1.7.6 Convex, concave and points of inflection (A-level only), 1.7.7 Differentiation from first principles for powers of x, 1.7.8 Differentiation from first principles for sin x and cos x (A-level only), 1.7.9 Differentiating x^n, 1.7.10 Differentiating e^(kx) and a^(kx) (A-level only), 1.7.11 Differentiating trigonometric functions (A-level only), 1.7.12 Derivative of ln x (A-level only), 1.7.13 Tangents and normals, 1.7.14 Stationary points, 1.7.15 Increasing and decreasing functions, 1.7.16 Points of inflection (A-level only), 1.7.17 Product and quotient rules (A-level only), 1.7.18 Chain rule (A-level only), 1.7.19 Parametric and implicit differentiation (A-level only), 1.7.20 Constructing differential equations (A-level only), and 1.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

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