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. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, 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.
