Explanation Given: The rate of unemployment of the country shortly after the Great Recession is, f ( t ) = 5 t + 300 t 2 + 25 (1) Where, ( 0 ≤ t ≤ 4 ) and the value t = 0 corresponds with the beginning of year 2010. Formula used: The quotient rule to differentiate the function f ( x ) = g ( x ) h ( x ) , where h ( x ) ≠ 0 is, d d x ( f ( x ) ) = d d x ( g ( x ) h ( x ) ) = h ( x ) d d x ( g ( x ) ) − g ( x ) d d x ( h ( x ) ) ( h ( x ) ) 2 Calculation: Use quotient rule to differentiate both side of the equation (1) with respect to t, to get the rate of change of unemployment of the country at the beginning of year 2010. d d t ( f ( t ) ) = d d t ( 5 t + 300 t 2 + 25 ) f ′ ( t ) = ( t 2 + 25 ) d d t ( 5 t + 300 ) − ( 5 t + 300 ) d d t ( t 2 + 25 ) ( t 2 + 25 ) 2 = ( t 2 + 25 ) ( 5 + 0 ) − ( 5 t + 300 ) ( 2 t + 0 ) ( t 2 + 25 ) 2 = ( t 2 + 25 ) ( 5 ) − ( 5 t + 300 ) ( 2 t ) ( t 2 + 25 ) 2 Further solve the above equation to get the rate of change of unemployment of the country at the beginning of year 2010

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 3.2, Problem 62E

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To find: The rate of change of unemployment of the country at the beginning of year 2013.

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Chapter 3.2, Problem 60E

Chapter 3.2, Problem 63E

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Applied Calculus for the Managerial, Life, and Social Sciences

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The rate of change of unemployment of the country at the beginning of year 2013.

Solution Summary: The author calculates the rate of change of unemployment of the country at the beginning of year 2013.

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To find: The rate of change of unemployment of the country at the beginning of year 2013.

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