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Differentiation

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Question 499

The temperature, TTT degrees Celsius, of a cooling laser component ttt minutes after activation is modeled by the function T=f(t)T = f(t)T=f(t) for t>0t > 0t>0.

It is given that:

  • the point P(4,10)P(4, 10)P(4,10) lies on the curve T=f(t)T = f(t)T=f(t)
  • the rate of change of temperature is f′(t)=12t+kt2f'(t) = 12\sqrt{t} + \frac{k}{t^2}f′(t)=12t​+t2k​, where kkk is a constant
  • the rate of change of temperature, f′(t)f'(t)f′(t), has a stationary point when t=4t = 4t=4
a.

Find the exact value of kkk.

[3]
b.

Determine an expression for f(t)f(t)f(t), giving your answer in its simplest form.

[5]
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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