11th Edition

ISBN: 9780135189405

Author: Michael Sullivan

Publisher: PEARSON

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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.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

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 2, Problem 26RE

In problems 25 and 26 , use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing.

f ( x ) = 2 x 4 − 5 x 3 + 2 x + 1 ( − 2 , 3 )

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Chapter 2, Problem 25RE

Chapter 2, Problem 27RE

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Chapter 2 Solutions

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In problems 25 and 26 , use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. f ( x ) = 2 x 4 − 5 x 3 + 2 x + 1 ( − 2 , 3 )

Solution Summary: The author explains how to determine the graph of the function f(x)=2x45, which has local maximum and minimum values, and determine where it is increasing and decreasing.

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Chapter 2 Solutions