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.
