   Chapter 2.8, Problem 19E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Let .f (x) = x2.(a) Estimate the values of f'(0), f ' ( 1 2 ) , f'(l) , and f'(2) by using a graphing device to zoom in on the graph of f.(b) Use symmetry to deduce the values of f ' ( − 1 2 ) , f'(– 1 ), and f'(–2).(c) Use the results from pans (a) and (b) to guess a formula for f'(x).(d) Use the definition of derivative to prove that your guess in part (c) is correct.

(a)

To determine

To estimate: The value of f(0), f(12), f(1) and f(2) by using a graphing device to zoom in on the graph of f.

Explanation

Given:

The function is f(x)=x2.

Estimation:

Obtain the value of f(x) at the point 0 as follows.

Use the online graphing calculator to zoom toward the point (0,0) as shown below in Figure 1.

The calculation of f(0) is as follows,

From Figure 1, the tangent to the curve at x=0 is the x-axis.

Thus, f(0)=0.

Obtain the value of f(x) at the point 12.

Use the online graphing calculator to zoom toward the point (12,14) as shown below in Figure 2.

The calculation of f(12) is as follows.

From Figure 2, the slope of the tangent line to the curve is computed as follows.

m=0.35360.1640.60360.4141

Thus, f(12)=1.

Obtain the value of f(x) at the point 1.

Use the online graphing calculator to zoom toward the point (1,1) as shown below in Figure 3

(b)

To determine

To deduce: The values of f(12),f(1) and f(2) using symmetry.

(c)

To determine

To guess: The formula for f by using part (a) and part (b).

(d)

To determine

To prove: The answer in part (c) is correct by using the definition of derivative.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Place the following set of n = 20 scores in a frequency distribution table.

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### Rationalize the denominator of 3x3x1 and simplify.

Mathematical Applications for the Management, Life, and Social Sciences

#### Write the following numbers in word form. 2.48

Contemporary Mathematics for Business & Consumers

#### What are the five steps of the scientific method?

Research Methods for the Behavioral Sciences (MindTap Course List) 