Explanation Given: Given the function f ( x ) = x 4 3 Given the function f ( x ) = x 4 3 First find the domain of the function x 4 3 = 0 The function has no undefined point therefore, the domain of the function ( − ∞ , 0 ) ∪ ( 0 , ∞ ) Now check the function on the domain, we see that At x > 0 , f ( x ) > 0 At x < 0 , f ( x ) < 0 Threfore, the function is positive on the interval ( 0 , ∞ ) and negative on the interval ( − ∞ , 0 ) . Now check weather the function is increasing and decreasing Find the first derivative of the function and equate its to zero to find the critical points . f ' ( x ) = 4 3 x 1 3 f ' ( x ) = 0 4 3 x 1 3 = 0 x = 0 Therefore, we get only one critical point

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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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 2SC

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The interval on which f is positive, negative, increasing, decreasing, concave up and concave down.

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Chapter 3, Problem 1SC

Chapter 3, Problem 3SC

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Chapter 3 Solutions

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The interval on which f is positive, negative, increasing, decreasing, concave up and concave down.

Solution Summary: The author explains that f is positive, negative, increasing, decreasing, concave up and down, and the function has no undefined point.

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The interval on which f is positive, negative, increasing, decreasing, concave up and concave down.

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Chapter 3 Solutions