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 9.8 Implicit Differentiation with exam-style questions for A Level Maths. 48 questions, 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.
