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9.8 Implicit Differentiation

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Question 22

A contour of the magnetic potential $U\,$ in a specialized laboratory setup is modeled by the curve with equation

x^5 y + 4x y^5 = 130

Prove that the curve does not intersect the coordinate axes.

[2]

bi.

Show that

\frac{dy}{dx} = -\frac{5x^4 y + 4y^5}{x^5 + 20xy^4}

[3]

bii.

Prove that the curve has no stationary points.

[3]

biii.

In the case when $x > 0$ , find the equation of the tangent line to the curve at the point where $y = 2$ . Give your answer in the form $a y + b x = c$ , where $c\,$ 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

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 22

A contour of the magnetic potential $U\,$ in a specialized laboratory setup is modeled by the curve with equation

x^5 y + 4x y^5 = 130

Prove that the curve does not intersect the coordinate axes.

[2]

bi.

Show that

\frac{dy}{dx} = -\frac{5x^4 y + 4y^5}{x^5 + 20xy^4}

[3]

bii.

Prove that the curve has no stationary points.

[3]

biii.

In the case when $x > 0$ , find the equation of the tangent line to the curve at the point where $y = 2$ . Give your answer in the form $a y + b x = c$ , where $c\,$ 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.