8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

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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Question

Chapter 3.2, Problem 107E

To determine

To graph:

The given function using a graphing utility.

Expert Solution

Answer to Problem 107E

The graph of our given function would be:

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 1

Explanation of Solution

Given:

A function: PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 2

Calculation:

Upon graphing the given functionusing a graphing utility, we will get our required graph as shown below:

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 3

To determine

To find:

The domain of the given function.

Expert Solution

Answer to Problem 107E

The domain of our given logarithmic function would be PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 4

Explanation of Solution

Given:

A function: PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 5

Calculation:

We know that logarithmic functions are not defined for negative values and radical functions are defined for non-negative numbers. To find domain of our given function, we will set argument of radical function greater than or equal to 0 as:

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 6

Therefore, the domain of our given logarithmic function would be PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 7 or

To determine

To find:

Open intervals on which the given function is increasing and decreasing using the graph of function.

Expert Solution

Answer to Problem 107E

The function is increasing on interval PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 9

Explanation of Solution

Given:

A function: PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 10

Calculation:

Upon looking at graph of our given function, we can see that the given function never decreases. The function is increasing from 1 to positive infinity.

Therefore, the function is increasing on interval PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 11

To determine

To approximate:

The relative maximum or minimum values of the function. Round to three decimal places.

Expert Solution

Answer to Problem 107E

The relative minimum of the given function is PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 12

Explanation of Solution

Given:

A function: PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 13

Calculation:

We can see from our given graph that there is no maximum value for our given function.

We can see that the minimum value of our given function occurs at PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 14 that is

Therefore, the relative minimum of the given function is PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 107E , additional homework tip 16

Chapter 3.2, Problem 106E

Chapter 3.2, Problem 108E

Chapter 3 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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Prob. 111CR Ch. 3 - Prob. 112CR Ch. 3 - Prob. 113CR Ch. 3 - Prob. 114CR Ch. 3 - Prob. 115CR Ch. 3 - Prob. 116CR Ch. 3 - Prob. 117CR Ch. 3 - Prob. 118CR Ch. 3 - Prob. 119CR Ch. 3 - Prob. 120CR Ch. 3 - Prob. 121CR Ch. 3 - Prob. 122CR Ch. 3 - Prob. 123CR Ch. 3 - Prob. 124CR Ch. 3 - Prob. 125CR Ch. 3 - Prob. 126CR Ch. 3 - Prob. 1CT Ch. 3 - Prob. 2CT Ch. 3 - Prob. 3CT Ch. 3 - Prob. 4CT Ch. 3 - Prob. 5CT Ch. 3 - Prob. 6CT Ch. 3 - Prob. 7CT Ch. 3 - Prob. 8CT Ch. 3 - Prob. 9CT Ch. 3 - Prob. 10CT Ch. 3 - Prob. 11CT Ch. 3 - Prob. 12CT Ch. 3 - Prob. 13CT Ch. 3 - Prob. 14CT Ch. 3 - Prob. 15CT Ch. 3 - Prob. 16CT Ch. 3 - Prob. 17CT Ch. 3 - Prob. 18CT Ch. 3 - Prob. 19CT Ch. 3 - Prob. 20CT Ch. 3 - Prob. 21CT Ch. 3 - Prob. 22CT Ch. 3 - Prob. 23CT Ch. 3 - Prob. 24CT Ch. 3 - Prob. 25CT Ch. 3 - Prob. 26CT Ch. 3 - Prob. 27CT Ch. 3 - Prob. 28CT Ch. 3 - Prob. 29CT Ch. 3 - Prob. 30CT Ch. 3 - Prob. 1STP Ch. 3 - Prob. 2STP Ch. 3 - Prob. 3STP Ch. 3 - Prob. 4STP Ch. 3 - Prob. 5STP Ch. 3 - Prob. 6STP Ch. 3 - Prob. 7STP Ch. 3 - Prob. 8STP Ch. 3 - Prob. 9STP Ch. 3 - Prob. 10STP Ch. 3 - Prob. 11STP Ch. 3 - Prob. 12STP Ch. 3 - Prob. 13STP Ch. 3 - Prob. 14STP Ch. 3 - Prob. 15STP Ch. 3 - Prob. 16STP Ch. 3 - Prob. 17STP Ch. 3 - Prob. 18STP Ch. 3 - Prob. 19STP Ch. 3 - Prob. 20STP Ch. 3 - Prob. 21STP Ch. 3 - Prob. 22STP Ch. 3 - Prob. 23STP Ch. 3 - Prob. 24STP Ch. 3 - Prob. 25STP Ch. 3 - Prob. 26STP

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