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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
