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GHW8 - f(c Find the open intervals where f is concave...

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Math 2413 Graded Homework # 8 GHW8 24 October 2011 Due Monday 10/31 in Lecture Work to be done in Blue book per syllabus Section 4.2: The Mean Value Theorem 1. (12 pts) Verify that the functions satisfy the hypotheses of the Mean Value Theorem on the given interval. Then ﬁnd all numbers c that satisfy the condition of the Mean Value Theorem ( a ) f ( x ) = x 3 - 3 x + 2 , [ - 2 , 2] ( b ) h ( x ) = ln x, [1 , 4] Section 4.3: How Derivatives Aﬀect the Shape of a Graph 2. (10 pts) For f ( x ) = x 4 + 8 x 3 + 200 (a) Find the open intervals on which f is increasing and the open intervals on which it is decreasing. (b) Find the local maximum and minimum values of
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Unformatted text preview: f . (c) Find the open intervals where f is concave upward and the open intervals where it is concave downward and ﬁnd its points of inﬂection. 3. (8 pts) For g ( x ) = 5 x 2 3-2 x 5 3 (a) Find the open intervals on which g is increasing and the open intervals on which it is decreasing. (b) Find the open intervals where g is concave upward and the open intervals where it is concave downward and ﬁnd its points of inﬂection. Section 4.4 Indeterminate Forms and L’Hospital’s Rule 4. (10) Evaluate lim x →∞ ± xe 1 x-x ² ....
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