L18 - f ( x ) on each of the intervals, and use the Test...

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Lecture 18: (Sec. 4.1) Increasing and Decreasing Functions ex. ex.
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def. A function f is increasing on an in- terval ( a,b ) if for any two values x 1 and x 2 in ( a,b ), whenever x 1 < x 2 , then def. A function f is decreasing on an in- terval ( a,b ) if for any two values x 1 and x 2 in ( a,b ), whenever x 1 < x 2 , then NOTE: f is increasing (decreasing) at a point c if there is an interval ( a,b ) con- taining c so that f is increasing (decreasing) on ( a,b ). ex.
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ex. For what intervals is f ( x ) = 4 - x 2 increasing and decreasing? NOTE: the graph of f 0 ( x ):
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Theorem: Test for Increasing and De- creasing Functions Let f be differentiable on the interval ( a,b ). 1) 2) 3) NOTE:
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ex. For what intervals is f ( x ) = x 2 / 3 in- creasing and decreasing? NOTE:
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def. Suppose y = f ( x ) is defined at x = c . Then c is a critical point(number) of f if 1) or 2) NOTE:
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To Determine the intervals on which a continuous function is increasing or decreasing 1) Find the critical points of f and find the open intervals determined by these points. 2) Determine the sign of
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Unformatted text preview: f ( x ) on each of the intervals, and use the Test for Increas-ing and Decreasing Functions to determine whether f is increasing or decreasing on each interval. ex. Given f ( x ) = x 3-3 2 x 2-6 x + 3. 1) Find all critical points of f . What are the coordinates of each point? 2) Find the open intervals on which f is increasing and decreasing. 3) Sketch the graph of f ( x ) = x 3-3 2 x 2-6 x + 3 ex. The position of a particle is given by the function s ( t ) = t 3-9 t 2 + 24 t where t is measured in minutes and s ( t ) is measured in yards. When is the particle moving for-ward? When is it moving backwards? ex. Consider the following graph of the derivative of a function f (so the graph is y = f ( x )). On what intervals is f in-creasing and decreasing?...
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This note was uploaded on 12/27/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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L18 - f ( x ) on each of the intervals, and use the Test...

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