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9.8 Implicit Differentiation

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Question 44

A chemical reaction's rate $R$ (measured in units/s) and the concentration $C$ of the substrate (measured in mmol/L) are related by the equation

R^3 + 5C^2 - 30RC = 0

The graph of this relationship for $\ge 0$ forms a loop in the first quadrant with a stationary point at $P$ , where the rate of change of $R$ with respect to $C$ is zero.

Show that at the point $P$ , the rate $R$ satisfies the equation

R^2(R - 45) = 0

[5]

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

[3]

Markscheme

9.8 Implicit Differentiation Questions

A Level
Maths
9.8 Implicit Differentiation

47 exam-style questions on Edexcel A Level Maths 9.8 Implicit Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

9.8 Implicit Differentiation

Question bank

9.8 Implicit Differentiation

Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Question 44

A chemical reaction's rate $R$ (measured in units/s) and the concentration $C$ of the substrate (measured in mmol/L) are related by the equation

R^3 + 5C^2 - 30RC = 0

The graph of this relationship for $\ge 0$ forms a loop in the first quadrant with a stationary point at $P$ , where the rate of change of $R$ with respect to $C$ is zero.

Show that at the point $P$ , the rate $R$ satisfies the equation

R^2(R - 45) = 0

[5]

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

[3]

Markscheme

9.8 Implicit Differentiation Questions

A Level
Maths
9.8 Implicit Differentiation

47 exam-style questions on Edexcel A Level Maths 9.8 Implicit Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.