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1.10 G: Differentiation

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Question 190

The intensity, III, of a specialized acoustic wave at a distance rrr from the source is modeled by the equation:

I=rsin⁡(2r),r>0,I>0 I = r^{\sin(2r)}, \quad r > 0, \quad I > 0 I=rsin(2r),r>0,I>0
a.

By first taking natural logarithms, find an expression for dIdr\frac{dI}{dr}drdI​ in terms of III and rrr.

[5]
b.

Hence show that at any stationary point of the intensity, the distance rrr must satisfy the equation:

tan⁡(2r)+2rln⁡r=0 \tan(2r) + 2r \ln r = 0 tan(2r)+2rlnr=0
[3]

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

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.

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