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Differentiation

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Question 125

A function f f\,f is defined by f(x)=x2x−4\displaystyle f(x) = \frac{x}{\sqrt{2x - 4}}f(x)=2x−4​x​

a.

State the maximum possible domain of fff.

[2]
b.

Use the quotient rule to show that f′(x)=x−4(2x−4)32\displaystyle f'(x) = \frac{x - 4}{(2x - 4)^{\frac{3}{2}}}f′(x)=(2x−4)23​x−4​

[3]
c.

Show that the graph of y=f(x)y = f(x)y=f(x) has exactly one point of inflection.

[7]
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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