The trajectory of a specialized particle in a particle accelerator is modeled by the curve C C\,C with equation
x=ye−4y,y∈Rx = y e^{-4y}, \quad y \in \mathbb{R}x=ye−4y,y∈R
Show that
dydx=yx(1−4y)\frac{\mathrm{d} y}{\mathrm{d} x} = \frac{y}{x(1 - 4y)}dxdy=x(1−4y)y
Given that a vertical detector strip at x=kx = kx=k, where k k\,k is a constant, detects the particle at exactly two distinct locations on the curve CCC,
find the range of possible values for kkk.
Practise Edexcel A Level Maths 9.7 Parametric Differentiation with exam-style questions for A Level Maths. 36 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.