14th Edition

ISBN: 9780135961438

Author: Barnett

Publisher: PEARSON CO

Concept explainers

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 4.1, Problem 57E

Chapter 4.1, Problem 57E, In Problems 57-60, use a graphing calculator to approximate the critical numbers of f(x) to two In Problems 57-60, use a graphing calculator to approximate the critical numbers of f(x) to two decimal places. Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema.

57. f(x) = x⁴ − 4x³ + 9x

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Chapter 4.1, Problem 56E

Chapter 4.1, Problem 58E

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Chapter 4 Solutions

EP CALCULUS FOR BUSINESS..-MYLAB ACCESS

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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In Problems 57 - 60 , use a graphing calculator to approximate the critical numbers of f ( x ) to two decimal places . Find the intervals on which f ( x ) is increasing, the intervals on which f ( x ) is decreasing, and the local extrema . 57. f ( x ) = x 4 − 4 x 3 + 9 x

Solution Summary: The author determines critical numbers, intervals on which f(x) is increasing or decreasing and local extrema by using online graphing calculator.

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Chapter 4 Solutions