CIE A Level Maths: Pure 1复习笔记5.2.2 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:

1. 1. Find the derivative f'(x)
   2. Solve the inequalities f'(x) ≥ 0 (for increasing intervals) and/or f'(x) ≤ 0 (for decreasing intervals)