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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 244

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∈R
a.

Show that

dydx=yx(1−5y) \frac{dy}{dx} = \frac{y}{x(1 - 5y)} dxdy​=x(1−5y)y​
[3]
b.

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.

[4]
Markscheme

3.6 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Differentiation (A-level only)

333 exam-style questions on WJEC A Level Maths 3.6 Differentiation (A-level only), covering 3.6.1 Differentiation (A-level only), 3.6.2 Differentiation (A-level only), 3.6.3 Differentiation (A-level only), 3.6.4 Differentiation (A-level only), 3.6.5 Differentiation (A-level only), 3.6.6 Differentiation (A-level only), 3.6.7 Differentiation (A-level only), and 3.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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