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Calculus Volume 1 | 18th Edition | ISBN: 9781938168024 | Authors: Openstax ISBN: 9781938168024 2035

Solution for problem 439 Chapter 5

Calculus Volume 1 | 18th Edition

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Calculus Volume 1 | 18th Edition | ISBN: 9781938168024 | Authors: Openstax

Calculus Volume 1 | 18th Edition

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Problem 439

True or False. Justify your answer with a proof or a counterexample. Assume all functions f and g are continuous over their domains.

If f(x)>0, \(f^{\prime}(x)>0\) for all x, then the righthand rule underestimates the integral \(\int_{a}^{b} f(x)\). Use a graph to justify your answer.

Text Transcription:

f^prime(x)>0

int_a^b f(x)

Step-by-Step Solution:
Step 1 of 3

Part 1 Introduction: Chapters 1-3 Definitions: Efficiency- society is getting the max benefits from its scarce resources. Equality- those benefits are distributed uniformly among society’s members. Opportunity cost- what you give up to get Assumptions; normally assume people are rational and they systematically and purposefully do the best they can to achieve their objectives, given the available opportunities. Marginal change- a small incremental adjustment to an existing plan of action. • a rational decision maker takes an action only if the marginal benefit exceeds the marginal cost. Incentives are crucial to analyzing how markets work: -a higher price provides an incentive for buyers to consume less and for sellers to produce more. -when policymakers fail to consider how their policies affect incentives, hey often end up with unintended consequences. i.e. seat belts reduce the benefits of careful driving, so people drive faster/less cautiously b/c they feel safer. Result of seat belt law is more accidents. Trade allows each person to specialize in the activities they do best. By trading, people can buy a greater variety of g/s at lower costs. In a market economy, the decisions of a central planner (communism) are replaced by the decisions of millions of firms/households. They interact in the market where prices & self-interest guide their decisions. -prices are instruments where the invisible hand directs economic activity. Prices reflect both the value of a good to society and the cost to society of m

Step 2 of 3

Chapter 5, Problem 439 is Solved
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Textbook: Calculus Volume 1
Edition: 18
Author: Openstax
ISBN: 9781938168024

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