How do you find the average rate of change of #f(x) = 1/x+6# from [2,2+h]?

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Answer 1 · 2017-10-04T18:27:54

# -1/(2(2+h)).#

Recall that, the Average Rate of Change (ARC) of a Function #f# on a

given interval #[a,b]# contained in the Domain of #f# is iven by,

#(f(b)-f(a))/(b-a).#

With, #f(x)=1/x+6, a=2, and, b=2+h,# we have,

#f(b)-f(a)=f(2+h)-f(2)={1/(2+h)+6}-{1/2+6},#

#=1/(2+h)-1/2={2-(2+h)}/(2(2+h))=-h/(2(2+h))............(1),# and,

#b-a=(2+h)-2=h............(2).#

From #(1), and (2),# we get the desired

#"The Reqd. ARC="-1/(2(2+h)).#