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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
