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−16Determine an expression for dydx\frac{dy}{dx}dxdy in terms of xxx and yyy.
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.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
