Explanation Given Information: The provided function is y = x 2 + 4 x 2 . Formula used: A vertical asymptote of a rational function h ( x ) = f ( x ) g ( x ) is x = a where g ( a ) = 0 and f ( a ) ≠ 0 . A horizontal asymptote of a rational function h ( x ) = f ( x ) g ( x ) is, Step 1. A line y = 0 if the degree of the numerator is less than the degree of the denominator. Step 2. The line y = a n b n ratio of the leading coefficients if the degree of the numerator is equal to the degree of the denominator. Step 3. Does not exist the degree of the numerator is greater than the degree of the denominator. To find relative maxima and minima of a function, 1. Set the first derivative of the function to zero f ' ( x ) = 0 , to find the critical values of the function. 2. Substitute the critical values into f ( x ) and calculate the critical points. 3. Calculate the sign of the function to the left and right of the critical values. If f ′ ( x ) < 0 and f ′ ( x ) > 0 on the left and right side respectively of a critical value, then the point is relative minimum. If f ′ ( x ) > 0 and f ′ ( x ) < 0 on the left and right side respectively of a critical value, then the point is relative maximum. Calculation: Consider the provided function, y = x 2 + 4 x 2 Recall that a vertical asymptote of a rational function h ( x ) = f ( x ) g ( x ) is x = a where, g ( a ) = 0 and f ( a ) ≠ 0 . Set the denominator x of the function equal to zero. x 2 = 0 x = 0 Substitute 0 for x in the numerator. x 2 + 4 = 0 2 + 4 = 0 + 4 = 4 ≠ 0 Thus, the vertical asymptote is the line x = 0 . Degree of the numerator is 2 and denominator is 2 of the function y = x 2 + 4 x 2 . Thus, the horizontal asymptote is the ratio of the leading coefficients. Since, the leading coefficient in the numerator is 1 and in the denominator is 1. Thus, the horizontal asymptote is y = 1 1 = 1 Now, calculate the first derivative of the function y = x 2 + 4 x 2 . y ' = x 2 ( 2 x ) − ( 2 x ) ( x 2 + 4 ) x 4 = 2 x 3 − x 3 − 4 x 4 = − 4 x 4 = ( x − 2 ) ( x + 2 ) x 2 Now, to obtain the critical values, set y ' = 0 as, − 4 x 4 = 0 − 4 = 0 Which is not possible

WebAssign Printed Access Card for Harshbarger/Reynolds' Mathematical Applications for the Management, Life, and Social Sciences, 12th Edition, Multi-Term

12th Edition

ISBN: 9781337630542

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 10.5, Problem 14E

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To calculate: The horizontal and vertical for the provided function y=x2+4x2 and sketch its graph.

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Chapter 10.5, Problem 13E

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Chapter 10 Solutions

WebAssign Printed Access Card for Harshbarger/Reynolds' Mathematical Applications for the Management, Life, and Social Sciences, 12th Edition, Multi-Term

Ch. 10.1 - 1. The x- values of critical points are found...Ch. 10.1 - Prob. 2CP Ch. 10.1 - Prob. 3CP Ch. 10.1 - Prob. 4CP Ch. 10.1 - In Problems 1 and 2, use the indicated points on...Ch. 10.1 - In Problems 1 and 2, use the indicated points on...Ch. 10.1 - 3. Use the graph of in Problem 1 to identify at...Ch. 10.1 - 4. Use the graph of in Problem 2 to identify at...Ch. 10.1 - In Problems 5 and 6, use the sign diagram for to...Ch. 10.1 - In Problems 5 and 6, use the sign diagram for to...

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The horizontal and vertical for the provided function y = x 2 + 4 x 2 and sketch its graph.

Solution Summary: The author calculates the horizontal and vertical asymptote of a rational function y=x2+4

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To calculate: The horizontal and vertical for the provided function y=x2+4x2 and sketch its graph.

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Chapter 10 Solutions