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Differentiation

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Question 30

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The depth of water in a storage tank, H H\,H metres, at time t t\,t hours after midnight is modelled by the equation

H=6+4cos⁡t2+sin⁡t,0≤t≤2π H = \frac{6 + 4 \cos t}{2 + \sin t}, \quad 0 \le t \le 2\pi H=2+sint6+4cost​,0≤t≤2π

The point M M\,M on the curve represents the time at which the water depth reaches its local minimum.

a.

Show that the ttt-coordinate of M M\,M is a solution of the equation

4sin⁡t+3cos⁡t=−2 4 \sin t + 3 \cos t = -2 4sint+3cost=−2
[4]
b.

Hence find, to 3 significant figures, the ttt-coordinate of MMM.

[4]
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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