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:
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.
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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