Given f(x) = x^{2} + 3x + 8, find the average rate of change of f(x) over each of the following pairs of intervals.

geduiwelh 2021-01-02 Answered
Given f(x)=x2+3x+8, find the average rate of change of f(x) over each of the following pairs of intervals.
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pattererX
Answered 2021-01-03 Author has 95 answers

Step 1
Given function is f(x)=x2+3x+8 Firstly, we will find the value of f(x)atx=1.9,1.99,2,2.1,2.01 f(1.9)=(1.9)2+3(1.9)+8=17.31
f(1.99)=(1.99)2+3(1.99)+8=17.9301
f(2)=(2)2+3(2)+8=18
f(2.01)=(2.01)2+3(2.01)+8=18.0701
f(2.1)=(2.1)2+3(2.1)+8=18.71
Step 2
Average rate of change of f(x) over [1.9, 2] is A1=f(2)f(1.9)21.9=1817.310.1=6.9 Average rate of change of f(x) over [1.99,2] is A2=f(2)f(1.99)21.99=1817.93010.01=6.99 Average rate of change of f(x) over [2,2.1] is A3=f(2.1)f(2)2.12=18.71180.1=7.1 Average rate of change of f(x) over [2,2.01] is A4=f(2.01)f(2)2.012=18.0701180.01=7.01
Step 3
(c) Instantaneous rate of change of f(x) at x=2is f(2)=limx2f(x)f(2)x2 From above parts as x approaches 2, f(x)f(2)x2 approaches 7. Therefore, Instantaneous rate of change of f(x) at z=2isf(2)=7 Step 4 Ans: Average rate of change of f(x) over [1.9,2] is 6.9 Average rate of change of f(x) over [1.99,2] is 6.99 Average rate of change of f(x) over [2,2.1] is 7.1 Average rate of change of f(x) over [2,2.01] is 7.01 Instantaneous rate of change of f(x) at x=2 is 7

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