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Differentiation

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Question 403

The movement of a precision robotic arm across a flat surface is defined by the parametric relationship

x=6cos⁡2y0≤x≤6,0≤y≤π4 x = 6 \cos 2y \quad 0 \le x \le 6, \quad 0 \le y \le \frac{\pi}{4} x=6cos2y0≤x≤6,0≤y≤4π​

where xxx is the horizontal position in millimetres and yyy is the control angle in radians.

a.

Find dxdy\frac{dx}{dy}dydx​ in terms of yyy.

[2]
b.

Hence show that

dydx=k36−x2 \frac{dy}{dx} = \frac{k}{\sqrt{36-x^2}} dxdy​=36−x2​k​

where kkk is a constant to be found.

[3]
c.

A specific calibration point P(a,b)P(a, b)P(a,b) lies on the path of the arm. Given that

  • the gradient of the path at PPP is −16-\frac{1}{6}−61​
  • both aaa and bbb are positive constants

find the exact values of aaa and bbb.

[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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