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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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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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 1.2, Problem 52E

Graph each function in Problems 49–54.

52. h ( x ) = { 10 + 2 x if 0 ≤ x ≤ 20 40 + 0.5 x if x > 20

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Chapter 1.2, Problem 51E

Chapter 1.2, Problem 53E

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Q1\ Let X be a topological space and let Int be the interior operation defined on P(X) such that 1₁.Int(X) = X 12. Int (A) CA for each A = P(X) 13. Int (int (A) = Int (A) for each A = P(X) 14. Int (An B) = Int(A) n Int (B) for each A, B = P(X) 15. A is open iff Int (A) = A Show that there exist a unique topology T on X. Q2\ Let X be a topological space and suppose that a nbhd base has been fixed at each x E X and A SCX show that A open iff A contains a basic nbdh of each its point Q3\ Let X be a topological space and and A CX show that A closed set iff every limit point of A is in A. A'S A ACA Q4\ If ẞ is a collection of open sets in X show that ẞ is a base for a topology on X iff for each x E X then ẞx = {BE B|x E B} is a nbhd base at x. Q5\ If A subspace of a topological space X, if x Є A show that V is nbhd of x in A iff V = Un A where U is nbdh of x in X.

Chapter 1 Solutions

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

Ch. 1.1 - Matched Problem 1 Sketch the graph of each...Ch. 1.1 - Matched Problem 2 Determine which of the following...Ch. 1.1 - Matched Problem 3 Find the domain of the function...Ch. 1.1 - Matched Problem 4 Use the functions in Example 4...Ch. 1.1 - Matched Problem 5 Find the domains of functions F,...Ch. 1.1 - Matched Problem 6 Repeat Example 6 for f(x) = x2 ...Ch. 1.1 - Matched Problem 7 The financial department in...Ch. 1.1 - To graph the equation y = x3 + 3x, we use...Ch. 1.1 - Prob. 2ED Ch. 1.1 - In Problems 18, use point-by-point plotting to...

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Graph each function in Problems 49–54 . 52. h ( x ) = { 10 + 2 x if 0 ≤ x ≤ 20 40 + 0.5 x if x > 20

Solution Summary: The author illustrates how the graph of the function h(x) is sketched below in Figure 1.

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Chapter 1 Solutions

Graph each function in Problems 49–54 . 52. h ( x ) = { 10 + 2 x if 0 ≤ x ≤ 20 40 + 0.5 x if x &gt; 20

Solution Summary: The author illustrates how the graph of the function h(x) is sketched below in Figure 1.

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Chapter 1 Solutions

Graph each function in Problems 49–54 . 52. h ( x ) = { 10 + 2 x if 0 ≤ x ≤ 20 40 + 0.5 x if x > 20