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)