The path of a specialized micro-drone as it ascends through a restricted aerodynamic corridor is modeled by a curve C C\,C in the xyxyxy-plane. The horizontal displacement xxx (in decametres) of the drone is related to its vertical height yyy (in decametres) by the equation x=ye−5y,y∈Rx = y e^{-5y}, \quad y \in \mathbb{R}x=ye−5y,y∈R
Show that dydx=yx(1−5y)\frac{dy}{dx} = \frac{y}{x(1 - 5y)}dxdy=x(1−5y)y
Given that the vertical line with equation x=kx = kx=k, where k k\,k is a constant, intersects C C\,C at exactly two points,
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.