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Differentiation

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Question 561

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

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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