3.5.4 Differentiation (A-level only)

Medium Hard

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Question 23

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]

3.5.4 Differentiation (A-level only) Questions

A Level
Maths
3.5.4 Differentiation (A-level only)

A Level
Maths CCEA
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