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Question 359

The diagram shows a sketch of the curve with equation x2−xy+2y2=12x^2 - xy + 2y^2 = 12x2−xy+2y2=12

Sketch of the curve and coordinate axes

a.

Show that dydx=2x−yx−4y\displaystyle \frac{dy}{dx} = \frac{2x - y}{x - 4y}dxdy​=x−4y2x−y​

[4]
b.

Show that y=2xy = 2xy=2x at the points on the curve where dydx=0\displaystyle \frac{dy}{dx} = 0dxdy​=0

[1]
c.

Hence find the points on the curve where dydx=0\displaystyle \frac{dy}{dx} = 0dxdy​=0

[4]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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