Table of Contents
Do open intervals have a maximum?
h(x) = x, 0 < x ≤ 1. The function h is continuous and defined on an open interval. It has neither an absolute maximum value nor an absolute minimum value.
Can there be a minimum on an open interval?
1. If there is an open interval containing c on which f(c) is a maximum, then f(c) is called a relative maximum of f. 2. If there is an open interval containing c on which f(c) is a minimum, then f(c) is called a relative minimum of f.
Can a function have no maximum or minimum?
Notice also that a function does not have to have any global or local maximum, or global or local minimum. Example: f(x)=3x + 4 f has no local or global max or min.
What is an open interval?
An open interval is one that does not include its endpoints, for example, {x | −3
Can there be more than 1 absolute maximum?
Important: Although a function can have only one absolute minimum value and only one absolute maximum value (in a specified closed interval), it can have more than one location (x values) or points (ordered pairs) where these values occur.
Which function has a maximum of 2 0?
Figure 8.
| Conclusion | ||
|---|---|---|
| 0 | 0 | Absolute maximum |
| 1 | -2 | Absolute minimum |
| 2 | -0.762 |
How do you know when there is no maximum?
Here are the rules:
- If the graph has a gap at the x value c, then the two-sided limit at that point will not exist.
- If the graph has a vertical asymptote and one side of the asymptote goes toward infinity and the other goes toward negative infinity, then the limit does not exist.
How do you find the minimum of a function on an interval?
Facts: Let f(x) be a function on [a, b] and c is a point in the interval [a, b]. (1) If for any point x in [a, b], f(x) ≥ f(c) (respectively, f(x) ≤ f(c)), then f(c) is the absolute (or global) minimum value (respectively, absolute (or global) local max- imum value) of f(x) on [a, b].
How do you show an open interval?
An open interval does not include its endpoints, and is indicated with parentheses. For example, (0,1) means greater than 0 and less than 1. This means (0,1) = {x | 0 < x < 1}. A closed interval is an interval which includes all its limit points, and is denoted with square brackets.
Is 0 an open set?
Since the point 0 cannot be an interior point of your set, the set {0} cannot be an open set.