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9.8 Implicit Differentiation

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Question 16

The relationship between the pressure $p$ and temperature $t$ of a specific gas model is described by the equation

p^3t + 2pt^3 = 12

Prove that the curve representing this relationship does not intersect the coordinate axes in the $p$ - $t$ plane.

[2]

bi.

Show that

\frac{dt}{dp} = -\frac{3p^2t + 2t^3}{p^3 + 6pt^2}

[3]

bii.

Prove that the model has no stationary points.

[3]

biii.

In the case when $p > 0$ , find the equation of the tangent line to the curve at the point where $t = 1$ . Give your answer in the form $a t + b p = c$ , where $a, b, c$ are integers.

[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

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Question 16

The relationship between the pressure $p$ and temperature $t$ of a specific gas model is described by the equation

p^3t + 2pt^3 = 12

Prove that the curve representing this relationship does not intersect the coordinate axes in the $p$ - $t$ plane.

[2]

bi.

Show that

\frac{dt}{dp} = -\frac{3p^2t + 2t^3}{p^3 + 6pt^2}

[3]

bii.

Prove that the model has no stationary points.

[3]

biii.

In the case when $p > 0$ , find the equation of the tangent line to the curve at the point where $t = 1$ . Give your answer in the form $a t + b p = c$ , where $a, b, c$ are integers.

[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.