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Unformatted text preview: f ′ ( x ) on each of the intervals, and use the Test for Increasing and Decreasing Functions to determine whether f is increasing or decreasing on each interval. Lecture 18 8 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? Lecture 18 9 2) Find the open intervals on which f is increasing and decreasing. Lecture 18 10 3) Sketch the graph of f ( x ) = x 3 − 3 2 x 2 − 6 x + 3 Lecture 18 11 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 forward? When is it moving backwards? Lecture 18 12 ex. Consider the following graph of the derivative of a function f (so the graph is y = f ′ ( x )). On what intervals is f increasing and decreasing?...
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 Spring '08
 Smith
 Calculus, Derivative, Continuous function

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