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Differentiation

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Question 577

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

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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