16th Edition

ISBN: 9781938168079

Author: Gilbert Strang, Edwin Jed Herman

Publisher: OpenStax

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 11E

Find the range of the functions.

11. g ( x , y ) = 16 − 4 x 2 − y 2

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Chapter 4.1, Problem 10E

Chapter 4.1, Problem 12E

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Chapter 4 Solutions

Calculus Volume 3

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