Microsoft_Word_-_MAC_2233__Increasing_an

Microsoft_Word_-_MAC_2233__Increasing_an - MAC 2233...

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MAC 2233 Increasing and Decreasing Functions Section 3.1 Definitions: 1. Increasing : A function is increasing if the y-values are getting larger from left to right. 2. Decreasing: A function is decreasing if the y-values are getting smaller from left to right. Examples: This is an Increasing Function. This is a Decreasing Function.
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Example: Determine the interval(s) on which f(x) is increasing or decreasing in interval notation. This function is increasing on the intervals ( ) 0 , 1 and ( ) , 1 . The function is decreasing on the intervals ( ) 1 , and ) 1 , 0 ( . Definition: 3. Critical Numbers and Critical Points : A number x = c in the domain of f(x) is called a critical number if either f’(x) = 0 or f’(x) does not exist. The point (c, f(c)) is called a critical point . Example: Find the critical numbers for f(x) = 2x 4 – 4x 2 + 1 h Find f’(x): f’(x) = 8x 3 – 8x h Solve f’(x) = 0 8x 3 – 8x = 0 8x(x 2 – 1) = 0 8x(x + 1)(x - 1) = 0 Critical numbers of x = 0, -1, 1
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Microsoft_Word_-_MAC_2233__Increasing_an - MAC 2233...

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