Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)

14th Edition

ISBN: 9780137400126

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

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Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

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Textbook Question

Chapter 4.2, Problem 91E

Production: point of diminishing returns. A T-shirt manufacturer is planning to expand its workforce. It estimates that the number of T-shirts produced by hiring x new workers is given by

T ( x ) = − 0.25 x 4 + 5 x 3 0 ≤ x ≤ 15

When is the rate of change of T-shirt production increasing and when is it decreasing? What is the point of diminishing returns and the maximum rate of change of T-shirt production? Graph T and T′ on the same coordinate system.

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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Chapter 4.2, Problem 90E

Chapter 4.2, Problem 92E

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Chapter 4 Solutions

Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)

Ch. 4.1 - Matched Problem 1 Repeat Example 1 for f(x) = x2 ...Ch. 4.1 - Matches Problem 2 Find the critical numbers of f,...Ch. 4.1 - Matched Problem 3 Find the critical numbers of f,...Ch. 4.1 - Matched Problem 4 Find the critical numbers of f,...Ch. 4.1 - Matched Problem 5 Find the critical numbers of f,...Ch. 4.1 - Prob. 6MP Ch. 4.1 - Matched Problem 7 Given f(x) = x3 9x2 + 24x 10,...Ch. 4.1 - Matched Problem 8 The graph in Figure 13...Ch. 4.1 - Matched Problem 9 The graph of the total revenue...Ch. 4.1 - Skills Warm-up Exercises In Problems 1-8, inspect...

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Solution Summary: The author calculates the local extrema for the revenue function T(x).

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Chapter 4 Solutions