O was 1. Why do we get a dilDifference quotient:0.6931712differenThis problem shows why radiansused in calculus.)67. The derivative of a functioline to the graph of f(x) aPhtangent line to f(x) = x2 + xction and this tangent line.100.693147In Problems 68-69, give an e10-6O.6931us rate of change of the funcI and at x = 2. What doIt the concavity of the graph10-868. A continuous functionpositive.0.6910-10069. A linear function with10-1244. (a) Let f(x) = x2. Explain what Table 2.5 tells usf(x) = x at x = 2Are the statements in Probabout f'(1).(b) Find f'(1) exactly.(c) If x changes by 0.1 near x 1, what does f'(1) tellus about how f(x) changes? Illustrate your answeruse your calculator to con-for 0 x 2. From your"(1).explanation for your answ2.3THE DERIVour calculator to approxi-f change of f at the pointx = x/4. (Note: Be suredians.)with a sketch.In theTable 2.5whata, in billions, can be ap-pointsDifference insuccessive x2 valuesXthe f0.998 0.996004006)'the0.0019970.999 0.998001ince the start of 2014.st was the population0.0019991.000 1.000000Example 1Estat the start of 2015?1.001 1.0020010.002001S4Ll 10people per year.1.002 1.0040040.002003fo, accessed April 1, 201598443/ns/today//us-population-hits-million-mark/#.VsuG1hgVmV0, accessed February 201.

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Asked Sep 10, 2019
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Please answer number 44.

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.
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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.

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Expert Answer

Step 1

 given

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f(x)x by differentiating function f (x) 2x by plugging the value of x 1 then f (1)2(1) f (1) =2

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Step 2

by plugging the value of x = 1 then

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f ()=2( f (1) 2

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Step 3

Table 2.5 tells that by moving towards 1 the value of the difference of the given function going to minimum....

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