# test 3 - Name Test#3 Applications of Derivatives Math 160...

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Name: _____________ Test #3: Applications of Derivatives Math 160 This is a calculus test. I need to see calculus in order to give credit. Show all work. If I don't see calculus work, I won't give credit. 1. f is continuous and a < b < c < . .. < k < l < m x a b c d e f g h i j k l m f '( x ) 0 + + + 0 + + + 0 ND f ''( x ) + + + 0 0 + 0 ND + lim x −∞ f x =∞ lim x ∞ f x =− 10 A. Where are the critical points for f ? B. Where does f have local extrema? For each one, identify it as a maximum or minimum. C. Where are the points of inflection of f ? D. Sketch a graph of f . E. How does f ( d ) compare to f ( h )? Bonus: Discuss whether or not f has any absolute extrema. (Under what conditions, on what intervals, whether it's possible, etc. Be as thorough as possible.) 2. Find the limit: lim x 0 e 3 x x 2 3 x 1 x 2 Bonus: lim x 0 + x p ln x for p > 0

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3. For the function g x = x x 1 When is g increasing? When is
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test 3 - Name Test#3 Applications of Derivatives Math 160...

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