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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 214

The height of a biological culture, H(t)H(t)H(t) millimetres, is observed over time t t\,t hours for t>0t > 0t>0.

Given that

  • H′(t)=10t14+kt2−4\displaystyle H'(t) = 10t^{\frac{1}{4}} + \frac{k}{t^2} - 4H′(t)=10t41​+t2k​−4, where k k\,k is a constant
  • H′′(t)=0H''(t) = 0H′′(t)=0 when t=16t = 16t=16
a.

Determine the value of kkk.

[3]
b.

Given also that

  • H(t)=20H(t) = 20H(t)=20 when t=1t = 1t=1

Find an expression for H(t)H(t)H(t), giving each term in simplest form.

[4]
Markscheme

3.6 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Differentiation (A-level only)

333 exam-style questions on WJEC A Level Maths 3.6 Differentiation (A-level only), covering 3.6.1 Differentiation (A-level only), 3.6.2 Differentiation (A-level only), 3.6.3 Differentiation (A-level only), 3.6.4 Differentiation (A-level only), 3.6.5 Differentiation (A-level only), 3.6.6 Differentiation (A-level only), 3.6.7 Differentiation (A-level only), and 3.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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