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3.6.6 Differentiation (A-level only)

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Question 27

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

3.6.6 Differentiation (A-level only) Questions

A Level
Maths
3.6.6 Differentiation (A-level only)

82 exam-style questions on WJEC A Level Maths 3.6.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

3.6.6 Differentiation (A-level only)

Question bank

3.6.6 Differentiation (A-level only)

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Question 27

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

3.6.6 Differentiation (A-level only) Questions

A Level
Maths
3.6.6 Differentiation (A-level only)

82 exam-style questions on WJEC A Level Maths 3.6.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.