Increasing & Decreasing Functions (CIE A Level Maths: Pure 1)

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Increasing & Decreasing Functions

What are increasing and decreasing functions?

  • A function f(x) is increasing on an interval [ab] if f'(x) ≥ 0 for all values of x such that ab.
    • If f'(x) > 0 for all x values in the interval then the function is said to be strictly increasing
    • In most cases, on an increasing interval the graph of a function goes up as x increases
  • A function f(x) is decreasing on an interval [ab] if f'(x) ≤ 0 for all values of x such that a b
    • If f'(x) < 0 for all x values in the interval then the function is said to be strictly decreasing
    • In most cases, on a decreasing interval the graph of a function goes down as x increases

 Incr Decr Illustr 1, A Level & AS Maths: Pure revision notes

  • To identify the intervals on which a function is increasing or decreasing you need to:
    1. Find the derivative f'(x)
    2. Solve the inequalities f'(x) ≥ 0 (for increasing intervals) and/or f'(x) ≤ 0 (for decreasing intervals)

Examiner Tip

  • On an exam, if you need to show a function is increasing or decreasing you can use either strict (<, >) or non-strict (≤, ≥) inequalities

Worked example

Incr Decr Example, A Level & AS Maths: Pure revision notes

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Roger

Author: Roger

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.