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1.10 G: Differentiation

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Question 156

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 at PPP
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]

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.

Question bank