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MATA32H3 (200)

Karimian Pour, C. (10)

Lecture 18

Department

MathematicsCourse Code

MATA32H3Professor

Karimian Pour, C.Lecture

18This

**preview**shows half of the first page. to view the full**2 pages of the document.** MATA32H3-Lec18-Extreme Value Theorem, Closed Interval Method, and

Concavity

Extreme Value Theorem (EVT)

Let y=f(x) be continuous [a,b]

Then f has both an absolute minimum and maximum on [a,b]

Two conditions of using EVT:

1. A closed interval

2. A function continuous on that interval

Ernest and Haussler, 2010

Closed Interval Method (CIM)

Assume y=f(x) is continuous on [a,b]

CIM is used to find where the minimum/ maximum is

1. Find all the critical points of f in [a,b]

2. Evaluate f(c) for each critical point in 1

3. Evaluate endpoints f(a) and f(b)

4. Absolute MAX=longest value from 2 to 3

Absolute MIN=shortest value from 2 to 3

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