Lesson21

# Lesson21 - MA 15200 I Lesson 21 Section 2.2 When describing...

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MA 15200 Lesson 21 Section 2.2 I Increasing, Decreasing, or Constant Functions A function is increasing if in an open interval, whenever 1 2 1 2 , then ( ) ( ) x x f x f x < < . The function values (or points on graph) are always rising. A function is decreasing if in an open interval, whenever 1 2 1 2 , then ( ) ( ) x x f x f x < > . The function values (or points on graph) are always falling . A function is constant if in an open interval, 1 2 ( ) ( ) f x f x = for any 1 2 and x x in the interval. The function values are equal and the graph is flat. When describing the interval where a function is increasing, decreasing, or constant; the intervals are open (no brackets) and you use the x -coordinates . II Relative Maxima and Relative Minima A function has a relative maximum value ( ) f a if there is an open interval containing a such that ( ) ( ) f a f x > for all x a in the open interval. In other words, the function value ( ) f a is larger than all other function values in that interval. Graphically, this is the function value of the highest point of the interval of the graph of the function. A function has a relative minimum value ( ) f b if there is an open interval containing b such that ( ) ( ) f b f x < for all x b in the open interval. In other words, the function value ( ) f b is smaller than all other function values in that interval. Graphically, this is

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Lesson21 - MA 15200 I Lesson 21 Section 2.2 When describing...

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