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3.6 Differentiation (A-level only)

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Question 15

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

x5y+4xy5=130 x^5 y + 4x y^5 = 130 x5y+4xy5=130
a.

Prove that the curve does not intersect the coordinate axes.

[2]
bi.

Show that

dydx=−5x4y+4y5x5+20xy4 \frac{dy}{dx} = -\frac{5x^4 y + 4y^5}{x^5 + 20xy^4} dxdy​=−x5+20xy45x4y+4y5​
[3]
bii.

Prove that the curve has no stationary points.

[3]
biii.

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

[4]
Markscheme

3.6 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Differentiation (A-level only)

332 exam-style questions on WJEC A Level Maths 3.6 Differentiation (A-level only), covering 3.6.1 Differentiation (A-level only), 3.6.2 Differentiation (A-level only), 3.6.3 Differentiation (A-level only), 3.6.4 Differentiation (A-level only), 3.6.5 Differentiation (A-level only), 3.6.6 Differentiation (A-level only), 3.6.7 Differentiation (A-level only), and 3.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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