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Increasing & Decreasing Functions (CIE A Level Maths: Pure 1)
Revision Note
Increasing & Decreasing Functions
What are increasing and decreasing functions?
- A function f(x) is increasing on an interval [a, b] if f'(x) ≥ 0 for all values of x such that a< x < b.
- 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 [a, b] if f'(x) ≤ 0 for all values of x such that a < x < 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
- To identify the intervals on which a function is increasing or decreasing you need to:
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- Find the derivative f'(x)
- 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
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