Absolute Extrema

Absolute Extrema

Learning Objectives:

Understand and apply Absolute Extrema

Math Tutoring on Absolute Extrema

Absolute Minimum and Absolute Maximum:

Suppose that f is a function with domain I.

f(c) is an Absolute Minimum if f(c) ≤ f(x) for all x in I.

f(c) is an Absolute Maximum if f(c) ≥ f(x) for all x in I.

Guidelines for Finding Absolute Extrema on a Closed Interval in Math Tutoring:

Suppose that f is a continuous function defined over a closed interval.

1.   Find the critical numbers of f in (a, b).

2.   Evaluate f at each critical number in (a, b).

3.   Evaluate f at each endpoint of [a, b].

4.   The least of these values is the minimum or Absolute Minimum. The greatest is the maximum or Absolute Maximum.

 

 

 

 

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Hook questions:

1.   How can we define Absolute Minimum and Absolute Maximum of a function?

2.   State the guidelines for finding Absolute Extrema on a closed interval.

 

 

 

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