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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Use the guidelines of Section 4.5 to sketch the curve.

y = 1 x + 1 + x

To determine

To Sketch: The curve by plotting x and y coordinates using guidelines.

Explanation

Given:

The Cartesian equation is as below.

y=1x+1+x (1)

Calculation:

  1. a)

Calculate the domain.

Refer the equation (1), the function is defined for all real values of x except for 1>x and 1<x as values under square root signs will be negative.

Hence, the domain of f(x) is [1,1].

  1. b)

Calculate the intercepts.

Calculate the value of x-intercept.

Substitute 0 for y in the equation (1).

0=1x+1+x1x=1+x

This is not possible for any value of x.

So x-intercept does not exists.

Substitute 0 for x in the equation (1).

y=10+1+0=2

Hence y-intercept is (0,2).

  1. c)

Calculate the symmetry.

Apply negative and positive values for x in the equation (1).

Substitute x in the equation (1).

f(x)=1x+1+xf(x)=1+x+1x

Hence, the condition f(x)=f(x) is true. So graph of f is symmetric about y-axis..

  1. d)

Calculate asymptotes.

Apply limit of x tends to (x) in the equation (1).

As the function is bounded on closed interval no asymptotes exist.

  1. e)

Calculate the intervals.

Differentiate the equation (1) with respect to x.

y=1x+1+xy=121x+121+x

Set y=0 to obtain critical points

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