lecture09

# lecture09 - 1 Maximum and Minimum Values This is all about...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Maximum and Minimum Values This is all about optimization problems. Definition 1. A function f has an absolute maximum at c if f ( c ) ≥ f ( x ) for x in the domain of f . f ( c ) is called the maximum value. A function has an absolute minimum at c if f ( c ) ≤ f ( x ) for all x in the domain of f . f ( c ) is called the minimum value. Maximum and minimum values are called extreme values. *Draw an example The problem is that not all functions have absolute minima or maxima. However, if we zoom in, a function might have a value that’s larger than those around it. *Draw an example Definition 2. A function f has a local maximum at c if f ( c ) ≥ f ( x ) when x is near c . f has a local minimum if f ( c ) ≤ f ( x ) when x is near c . x is near c if there’s some interval around c where the statement is true. Example 1.1. f ( x ) = cos x f ( x ) = x 2 f ( x ) = 3 x 4- 16 x 3 + 18 x 2 How can we tell if a function has an extreme value or not? With a theorem, of course. Extreme Value Theorem. If f is continuous on a closed interval [ a, b ], then f attains an absolute maximum value f ( c ) and an absolute minimum f ( d ) for some values c and d in [ a, b ]....
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

lecture09 - 1 Maximum and Minimum Values This is all about...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online