AQA A Level Maths: Pure復習筆記7.2.2 Increasing & Decreasing Functions
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)
Exam 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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