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section 2.5 The Graph of a Function

1 a global maximum for f on d is a point c in d such

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Unformatted text preview: D is a point c in D such that f (x ) ≤ f (c ) for all x ∈ D . 2 A global minimum for f on D is a point c in D such that f (x ) ≥ f (c ) for all x ∈ D . 3 If there is an interval i in D containing c such that f (c ) is a maximum on I , then we call f (c ) a local maximum of f . 4 If there is an interval I in D containing c such that f (c ) is a minimum on I , then we call f (c ) a local minimum of f . Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Difference Quotient Example Discuss the local and global maximums and Minimums of the function graphed below. Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Difference Quotient The Difference Quotient Definition Suppose f is a function from D into R. The difference quotient of f over an interval [a, b ] in in D is: ∆y f (b ) − f (a) f (x + h) − f (x ) = = ∆x b−a h where h = b − a and a = x . Example Compute and simplify the difference quotient of: 1 2 f (x ) = x 2 − 3. 4 f (x ) = . x...
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