The trajectory of a specialized particle in a particle accelerator is modeled by the curve C C\,C with equation
x=ye−4y,y∈R x = y e^{-4y}, \quad y \in \mathbb{R} x=ye−4y,y∈RShow that
dydx=yx(1−4y) \frac{\mathrm{d} y}{\mathrm{d} x} = \frac{y}{x(1 - 4y)} dxdy=x(1−4y)yGiven 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 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.
