12th Edition

ISBN: 9780134773285

Author: MULLINS

Publisher: YUZU

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 12.3, Problem 8E

Find the locations of the absolute extrema of each function on the given interval. (See Examples 2 and 3.)

f ( x ) = 2 x 3 − 3 x 2 − 12 x + 4 ; [ − 2 , 0 ]

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Chapter 12.3, Problem 7E

Chapter 12.3, Problem 9E

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Chapter 12 Solutions

EBK MATHEMATICS WITH APPLICATIONS IN TH

Ch. 12.1 - Checkpoint 1 For what values of x is the function...Ch. 12.1 - Checkpoint 2 Find all intervals on which is...Ch. 12.1 - Checkpoint 3 Identity the x-values of all points...Ch. 12.1 - Checkpoint 4 Find the critical numbers for each of...Ch. 12.1 - Prob. 5CP Ch. 12.1 - Prob. 6CP Ch. 12.1 - Checkpoint 7 Find the locations of the local...Ch. 12.1 - Prob. 8CP Ch. 12.1 - Checkpoint 9 If a sales function is given by...Ch. 12.1 - Prob. 1E

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Find the locations of the absolute extrema of each function on the given interval. (See Examples 2 and 3.) f ( x ) = 2 x 3 − 3 x 2 − 12 x + 4 ; [ − 2 , 0 ]

Solution Summary: The author explains that the function f(x) has an absolute maxima at x=-1 and a absolute minima.

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Chapter 12 Solutions