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∈R x = y e^{-5y}, \quad y \in \mathbb{R} x=ye−5y,y∈RShow that
dydx=yx(1−5y) \frac{dy}{dx} = \frac{y}{x(1 - 5y)} dxdy=x(1−5y)yGiven 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 Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, 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.
