# The arrange the following numbers in increasing order and reasoning. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2.6, Problem 17E
To determine

## To find: The arrange the following numbers in increasing order and reasoning.

Expert Solution

The arrangement of the following numbers in increasing order is g(0)<0<g(4)<g(2)<g(2).

### Explanation of Solution

Result used:

The slope of the line passing through the points (x1,y1) and (x2,y2) is y2y1x2x1.

Calculation:

Obtain the values g(2).

From the given graph, draw the tangent line at x=2 is approximately joining the points (2,0) and (2.2,0.3).

Use the slope formula stated above and compute the slope of the line passing through the points (2,0) and (2.2,0.3).

g(2)=0.302.2+2=0.30.2=0.30.2=1.5

Thus, the value is g(2)=1.5.

Obtain the values g(0).

From the given graph, draw the tangent line at x=0 is approximately joining the points (0,0) and (0.1,0.1).

Use the slope formula stated above and compute the slope of the line passing through the points (0,0) and (0.1,0.1).

g(0)=0.100.1+0=0.10.1=1

Thus, the value is g(0)=1.

Obtain the values g(2).

From the given graph, draw the tangent line at x=2 is approximately joining the points (2,0) and (1.9,0.1).

Use the slope formula stated above and compute the slope of the line passing through the points (2,0) and (1.9,0.1).

g(2)=0.101.92=0.10.1=1

Thus, the value is g(2)=1.

Obtain the values g(4).

From the given graph, draw the tangent line at x=4 is approximately joining the points (4,3) and (3.7,2.8).

Use the slope formula stated above and compute the slope of the line passing through the points (4,3) and (3.7,2.8).

g(4)=2.833.74=0.20.3=0.20.3=0.6

Thus, the value is g(4)=0.4.

Therefore, the arrangement of the following numbers in increasing order is g(0)<0<g(4)<g(2)<g(2)

From graph it is observe that the highest value of the slope is g(2)=1.5 and the smallest value of the slope is g(0)=1.

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