To determine To find: The intervals, where the rate of change of function increases and decreases, also the diminishing returns and the maximum value; sketch the graph of the function. Explanation Given: The number of T-shirts to be produced by the company by extending its workforce is estimated as follows, T ( x ) = − 0.25 x 4 + 5 x 3 Where, x denotes the number of workers. The expanding workforce varies from 0 to 15 workers. Calculation: The local extrema for the revenue function T ( x ) is obtained as follows. From the given, the domain of the function is ( 0 , 15 ) . Obtain the derivative of the function T ( x ) as follows. T ′ ( x ) = d d x ( − 0.25 x 4 + 5 x 3 ) = − 1 x 3 + 15 x 2 Obtain the second derivative of the function as follows. T ′ ′ ( x ) = d d x ( − 1 x 3 + 15 x 2 ) = − 3 x 2 + 30 x = − 3 x ( x − 10 ) Equate T ′ ′ ( x ) to 0 in order to obtain its partition numbers. − 3 x ( x − 10 ) = 0 x = 0 and x = 10 Thus, the partition numbers of the function are x = 0 and x = 10 . The sign chart for T ′ ( x ) and T ′ ′ ( x ) is as shown below in Table 1. Interval Test number T ′ ( x ) T ′ ′ ( x ) T ′ ( x ) T ( x ) 0 < x < 10 1 T ′ ( 1 ) = − 1 ( 1 ) 3 + 15 ( 1 ) 2 = − 1 + 15 = 14 T ′ ( x ) > 0 T ′ ′ ( 1 ) = − 3 ( 1 ) 2 + 30 ( 1 ) = − 3 + 30 = 27 T ′ ′ ( x ) > 0 Increasing Concave upward x = 10 10 T ′ ( 10 ) = − 1 ( 10

COLL.MATH F/BUS ECO.(LL+18 WEEK MYLAB E)

14th Edition

ISBN: 9780135998083

Author: Barnett

Publisher: PEARSON

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Chapter 11.2, Problem 91E

To determine

To find: The intervals, where the rate of change of function increases and decreases, also the diminishing returns and the maximum value; sketch the graph of the function.

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Chapter 11.2, Problem 90E

Chapter 11.2, Problem 92E

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COLL.MATH F/BUS ECO.(LL+18 WEEK MYLAB E)

Ch. 11.1 - Matched Problem 1 Repeat Example 1 for f(x) = x2 –...Ch. 11.1 - Matches Problem 2 Find the critical numbers of f,...Ch. 11.1 - Matched Problem 3 Find the critical numbers of f,...Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 7MP Ch. 11.1 - Prob. 8MP Ch. 11.1 - Prob. 9MP Ch. 11.1 - Skills Warm-up Exercises In Problems 1-8, inspect...

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