AQA A Level Maths: Pure复习笔记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

7.2.2-Incr-Decr-Illustr-1

  • 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)

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

7.2.2-Incr-Decr-Example

 

 

 

 

 

 

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