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Differentiation - Increasing and Decreasing Functions

Differentiation - Increasing and Decreasing Functions

TGM Original Questions

A function has the equation \(f(x) = x - \frac{2}{3x - 1}\).

  1. Find the range of values of \(x\) for which the function to be valid.
  2. Explain why the graph of \(f(x)\) does not have a stationary point.
  3. Hence state whether \(f(x)\) is an increasing or decreasing function.

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Answer:(i) \(x\ne\dfrac13\) (ii) \(f'(x)=1+\dfrac{6}{(3x-1)^2}\ne0\) (iii) Increasing on each interval \(x<\dfrac13\) and \(x>\dfrac13\)

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