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Differentiation

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Question 475

A robotic welding tool follows a path in the xyxyxy-plane described by the implicit equation

3y2−12y=4x2+16x−16 3y^2 - 12y = 4x^2 + 16x - 16 3y2−12y=4x2+16x−16
a.

Determine an expression for dydx\frac{dy}{dx}dxdy​ in terms of xxx and yyy.

[3]
b.

The path of the tool is discontinuous, and it cannot operate within an exclusion zone defined by the xxx-interval (p,q)(p, q)(p,q).

By considering the points on the curve where the tangent is vertical, find the exact values of ppp and qqq.

[5]
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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