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Differentiation

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Question 62

The curve C C\,C with equation f(x)=sin⁡2xekx\displaystyle f(x) = \frac{\sin 2x}{e^{kx}}f(x)=ekxsin2x​ −π<x<π-\pi < x < \pi−π<x<π, where k k\,k is a positive constant, is shown in the diagram.

The xxx-coordinates of the turning points of C C\,C satisfy the equation tan⁡2x=1\tan 2x = 1tan2x=1.

Sketch of curve C on −π < x < π with horizontal x- and vertical y-axes.

a.

Show that k=2k = 2k=2

[6]
b.

Hence find the coordinates of the turning points

[3]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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