O was 1. Why do we get a dil Difference quotient: 0.6931712 differen This problem shows why radians used in calculus.) 67. The derivative of a functio line to the graph of f(x) a Ph tangent line to f(x) = x2 + x ction and this tangent line. 10 0.693147 In Problems 68-69, give an e 10-6 O.6931 us rate of change of the func I and at x = 2. What do It the concavity of the graph 10-8 68. A continuous function positive. 0.69 10-10 0 69. A linear function with 10-12 44. (a) Let f(x) = x2. Explain what Table 2.5 tells us f(x) = x at x = 2 Are the statements in Prob about f'(1). (b) Find f'(1) exactly. (c) If x changes by 0.1 near x 1, what does f'(1) tell us about how f(x) changes? Illustrate your answer use your calculator to con- for 0 x 2. From your "(1). explanation for your answ 2.3 THE DERIV our calculator to approxi- f change of f at the point x = x/4. (Note: Be sure dians.) with a sketch. In the Table 2.5 what a, in billions, can be ap- points Difference in successive x2 values X the f 0.998 0.996004 006)' the 0.001997 0.999 0.998001 ince the start of 2014. st was the population 0.001999 1.000 1.000000 Example 1 Est at the start of 2015? 1.001 1.002001 0.002001 S4Ll 10 people per year. 1.002 1.004004 0.002003 fo, accessed April 1, 2015 98443/ns/today//us-population-hits-million-mark/#.VsuG1hgVmV0, accessed February 201.
O was 1. Why do we get a dil Difference quotient: 0.6931712 differen This problem shows why radians used in calculus.) 67. The derivative of a functio line to the graph of f(x) a Ph tangent line to f(x) = x2 + x ction and this tangent line. 10 0.693147 In Problems 68-69, give an e 10-6 O.6931 us rate of change of the func I and at x = 2. What do It the concavity of the graph 10-8 68. A continuous function positive. 0.69 10-10 0 69. A linear function with 10-12 44. (a) Let f(x) = x2. Explain what Table 2.5 tells us f(x) = x at x = 2 Are the statements in Prob about f'(1). (b) Find f'(1) exactly. (c) If x changes by 0.1 near x 1, what does f'(1) tell us about how f(x) changes? Illustrate your answer use your calculator to con- for 0 x 2. From your "(1). explanation for your answ 2.3 THE DERIV our calculator to approxi- f change of f at the point x = x/4. (Note: Be sure dians.) with a sketch. In the Table 2.5 what a, in billions, can be ap- points Difference in successive x2 values X the f 0.998 0.996004 006)' the 0.001997 0.999 0.998001 ince the start of 2014. st was the population 0.001999 1.000 1.000000 Example 1 Est at the start of 2015? 1.001 1.002001 0.002001 S4Ll 10 people per year. 1.002 1.004004 0.002003 fo, accessed April 1, 2015 98443/ns/today//us-population-hits-million-mark/#.VsuG1hgVmV0, accessed February 201.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
Related questions
Concept explainers
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
Topic Video
Question
Please answer number 44.
Transcribed Image Text:O was 1. Why do we get a dil
Difference quotient:
0.6931712
differen
This problem shows why radians
used in calculus.)
67. The derivative of a functio
line to the graph of f(x) a
Ph
tangent line to f(x) = x2 + x
ction and this tangent line.
10
0.693147
In Problems 68-69, give an e
10-6
O.6931
us rate of change of the func
I and at x = 2. What do
It the concavity of the graph
10-8
68. A continuous function
positive.
0.69
10-10
0
69. A linear function with
10-12
44. (a) Let f(x) = x2. Explain what Table 2.5 tells us
f(x) = x at x = 2
Are the statements in Prob
about f'(1).
(b) Find f'(1) exactly.
(c) If x changes by 0.1 near x 1, what does f'(1) tell
us about how f(x) changes? Illustrate your answer
use your calculator to con-
for 0 x 2. From your
"(1).
explanation for your answ
2.3
THE DERIV
our calculator to approxi-
f change of f at the point
x = x/4. (Note: Be sure
dians.)
with a sketch.
In the
Table 2.5
what
a, in billions, can be ap-
points
Difference in
successive x2 values
X
the f
0.998 0.996004
006)'
the
0.001997
0.999 0.998001
ince the start of 2014.
st was the population
0.001999
1.000 1.000000
Example 1
Est
at the start of 2015?
1.001 1.002001
0.002001
S4Ll 10
people per year.
1.002 1.004004
0.002003
fo, accessed April 1, 2015
98443/ns/today//us-population-hits-million-mark/#.VsuG1hgVmV0, accessed February 201.
Expert Solution
Trending now
This is a popular solution!
Step by step
Solved in 10 steps with 8 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage