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Determine from the graphs whether f has a minimum in the open interval (a, b).

Question:

Determine from the graphs whether f has a minimum in the open interval (a, b).

Infimum and Minimum

Given a non empty set then we define k to be an infimum of A if and only if {eq}k \leq x {/eq} for all {eq}x \in A {/eq}.

A minimum of A is any number M such that M is an infimum of A and {eq}M \in A {/eq} .

So, not every infimum is a minimum but every minimum is an infimum. For an infimum to be a minimum of some set it must be a member of the set.

Also, if a set is bounded from below then the set has a infimum.

Answer and Explanation:

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For graph I, according to the definitions of infimum and minimum, we can notice that the function has an infimum (the little white circle on the...

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Minimum Values: Definition & Concept

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Chapter 18 / Lesson 16
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The minimum value of a quadratic function is the low point at which the function graph has its vertex. This lesson will define minimum values and give some example problems for finding those values. A quiz will complete the lesson.


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