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9.8 Implicit Differentiation

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Question 18

A chemical reaction's equilibrium state is represented by a curve $C$ with the equation

2^x - xy + y^2 = 28, \quad y \ge 0

where $x$ and $y$ represent the concentrations of two specific reagents in mol dm $^{-3}$ . A specific experimental state $P$ lies on $C$ where the concentration $x = 4$ .

Find the concentration $y$ at state $P$ .

[2]

Find $dydx\frac{\text{d}y}{\text{d}x}$ in terms of $x$ and $y$ .

[3]

The tangent to $C$ at $P$ intersects the $x$ -axis at the point $Q$ .

Find the $x$ -coordinate of $Q$ , giving your answer in the form $aln⁡2+bcln⁡2+d\frac{a \ln 2 + b}{c \ln 2 + d}$ where $a, b, c$ and $d$ are integers to be found.

[4]

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 18

A chemical reaction's equilibrium state is represented by a curve $C$ with the equation

2^x - xy + y^2 = 28, \quad y \ge 0

where $x$ and $y$ represent the concentrations of two specific reagents in mol dm $^{-3}$ . A specific experimental state $P$ lies on $C$ where the concentration $x = 4$ .

Find the concentration $y$ at state $P$ .

[2]

Find $dydx\frac{\text{d}y}{\text{d}x}$ in terms of $x$ and $y$ .

[3]

The tangent to $C$ at $P$ intersects the $x$ -axis at the point $Q$ .

Find the $x$ -coordinate of $Q$ , giving your answer in the form $aln⁡2+bcln⁡2+d\frac{a \ln 2 + b}{c \ln 2 + d}$ where $a, b, c$ and $d$ are integers to be found.

[4]

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.