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1.10 G: Differentiation

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Question 199

The output signal RRR, measured in millivolts, of a high-precision sensor is modeled by the function

R(t)=12tln⁡(4t)t>0 R(t) = 12\sqrt{t} \ln(4t) \quad t > 0 R(t)=12t​ln(4t)t>0

where ttt is the time in milliseconds after the sensor is triggered. The signal is zero at time TTT.

a.

State the value of TTT.

[1]
b.

The signal reaches its minimum value at the point MMM.

Use calculus to find the exact coordinates of MMM.

[5]
c.

Hence find the range of the function S(t)S(t)S(t) where

S(t)=−5R(t) S(t) = -5R(t) S(t)=−5R(t)
[2]
Markscheme

1.10 G: Differentiation Questions

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

375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, 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). Each one has a worked solution and a mark scheme showing where the marks go.

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