# 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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Step 1

given

Step 2

by plugging the value of x = 1 then

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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