http://www.ck12.org Chapter 1. Functions and Graphs
Solution: Since the function seems to abruptly end at the end points and does not go beyond the display, the
endpoints are important.
There is a global minimum at (0, 0). There is a local maximum at (-1, 1) and a global maximum at (5, 5).
Example C
Identify and categorize all extrema.
Solution:Since this function appears to increase to the right as indicated by the arrow there is no global maximum.
There are not any other high points either, so there are no local maximums. There is only the end point at (0, 0)
which is a global minimum.
Concept Problem Revisited
Maximums and minimums should be intuitive because they simply identify the highest points and the lowest points,
or the peaks and the valleys, in a graph. There is a formal distinction about whether a maximum is the highest on
some local open interval (does not matter how small), or whether it is simply the highest overall.
Vocabulary
Global extremaandabsolute extremaare synonyms that refer to the points with theyvalues that are either the
highest or the lowest of the entire function.
Local extremaandrelative extremaare synonyms that refer to the points with theyvalues that are the highest or
lowest of a local neighborhood of the function.
Guided Practice
- Identify and categorize all extrema.