(A) To determine To find: The local extrema of the revenue function of the company. Explanation Given: The demand of the new ice cream found by the marketing research department of the company is as follows, p = 10 e − x Where p and x (thousand quarts) denotes the price and sales of the ice cream per week, respectively. The demand varies from 0 to 5 thousand quants per week. Calculation: The weekly revenue function of the company is calculated as R ( x ) = x p . That is, R ( x ) = x 10 e − x . The local extrema for the revenue function R ( x ) is obtained as follows. From the given, the domain of the function is ( 0 , 5 ) . Obtain the derivative of the function R ( x ) as follows. R ′ ( x ) = 10 d d x ( x e − x ) = 10 [ 1 ( e − x ) + ( − e − x ) ( x ) ] = 10 [ e − x − x e − x ] To obtain the critical points, find the points where the first derivative become zero or undefined. Equate R ′ ( x ) to 0 in order to obtain its partition numbers. 10 [ e − x − x e − x ] = 0 e − x = x e − x x = 1 The partition number of R ′ ( x ) is at x = 1 . The critical numbers of R ( x ) are the partition numbers of R ′ ( x ) (B) To determine To find: The intervals where the function is concave upward and concave downward.

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14th Edition

ISBN: 9780137553341

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Chapter 11.2, Problem 89E

(A)

To determine

To find: The local extrema of the revenue function of the company.

(B)

To determine

To find: The intervals where the function is concave upward and concave downward.

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Chapter 11.2, Problem 88E

Chapter 11.2, Problem 90E

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Chapter 11 Solutions

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

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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