Explanation Given information: The given function is f ( x ) = x e x Concept used: Concepts of derivatives: If f ′ is positive, f is increasing If f ′ is negative, f is decreasing If f ′ is zero, f is constant If f ″ is positive, f is concave up if f ″ is negative, then f is concave down. To find the local extrema use the following second derivative test: Suppose x = c is the location of a critical point of a function f with f ′ ( c ) = 0 ,and suppose both f and f ′ are differentiable and f ″ is continuous on an interval around x = c . If f ″ ( c ) is positive, then f has a local minimum at x = c If f ″ ( c ) is negative, then f has a local maximum at x = c If f ″ ( c ) = 0 , then this test says nothing about whether or not f has extremum at

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 3, Problem 21SC

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To construct: the sign charts for f,f′ and f″ . To examine: the limits at any interesting values and at ±∞ . To interpret the information to sketch the graph of f .

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Chapter 3, Problem 20SC

Chapter 3, Problem 22SC

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Chapter 3 Solutions

Calculus

Ch. 3.1 - Prob. 1TB Ch. 3.1 - Prob. 0C Ch. 3.1 - Prob. 1C Ch. 3.1 - Prob. 2C Ch. 3.1 - Prob. 3C Ch. 3.1 - Prob. 4C Ch. 3.1 - Prob. 5C Ch. 3.1 - Prob. 6C Ch. 3.1 - Prob. 7C Ch. 3.1 - Prob. 8C

Ch. 3.1 - Prob. 9C Ch. 3.1 - Prob. 10C Ch. 3.1 - Prob. 11C Ch. 3.1 - Prob. 12C Ch. 3.1 - Prob. 13C Ch. 3.1 - Prob. 14C Ch. 3.1 - Prob. 15C Ch. 3.1 - Prob. 16C Ch. 3.1 - Prob. 17C Ch. 3.1 - Prob. 18C Ch. 3.1 - Prob. 19C Ch. 3.1 - Prob. 20C Ch. 3.1 - Prob. 21C Ch. 3.1 - Prob. 22C Ch. 3.1 - Prob. 23S Ch. 3.1 - Prob. 24S Ch. 3.1 - Prob. 25S Ch. 3.1 - Prob. 26S Ch. 3.1 - Prob. 27S Ch. 3.1 - Prob. 28S Ch. 3.1 - Prob. 29S Ch. 3.1 - Prob. 30S Ch. 3.1 - Prob. 31S Ch. 3.1 - Prob. 32S Ch. 3.1 - Prob. 33S Ch. 3.1 - Prob. 34S Ch. 3.1 - Prob. 35S Ch. 3.1 - Prob. 36S Ch. 3.1 - Prob. 37S Ch. 3.1 - Prob. 38S Ch. 3.1 - Prob. 39S Ch. 3.1 - Prob. 40S Ch. 3.1 - Prob. 41S Ch. 3.1 - Prob. 42S Ch. 3.1 - Prob. 43S Ch. 3.1 - Prob. 44S Ch. 3.1 - Prob. 45S Ch. 3.1 - Prob. 46S Ch. 3.1 - Prob. 47S Ch. 3.1 - Prob. 48S Ch. 3.1 - Prob. 49S Ch. 3.1 - Prob. 50S Ch. 3.1 - Prob. 51S Ch. 3.1 - Prob. 52S Ch. 3.1 - Prob. 53S Ch. 3.1 - Prob. 54S Ch. 3.1 - Prob. 55S Ch. 3.1 - Prob. 56S Ch. 3.1 - Prob. 57S Ch. 3.1 - Prob. 58S Ch. 3.1 - 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To construct: the sign charts for f , f ′ and f ″ . To examine: the limits at any interesting values and at ± ∞ . To interpret the information to sketch the graph of f .

Solution Summary: The author explains how to construct the sign charts for f,fprime, and to examine the limits at any interesting values.

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To construct: the sign charts for f,f′ and f″ . To examine: the limits at any interesting values and at ±∞ . To interpret the information to sketch the graph of f .

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Chapter 3 Solutions