Question #f87f1

1 Answer
Jim G.
Oct 26, 2017

#-7/(a(a+h))#

Explanation:

#"the average rate of change of a function f(x) over an "#
#"interval between 2 points is the slope of the "#
#color(blue)"secant line"" connecting the 2 points"#

#"average rate of change "=(f(b)-f(a))/(b-a)#

#"in the closed interval "[a,b]#

#"here "a=a" and "b=a+h#

#rArrf(b)=f(a+h)=7/(a+h)#

#rArrf(a)=7/a#

#"average rate of change "=(7/(a+h)-7/a)/(a+h-a)#

#=((7a)/(a(a+h))-(7(a+h))/(a(a+h)))/h#

#=(7a-7a-7h)/(ha(a+h))#

#=(-7h)/(ha(a+h)#

#=-7/(a(a+h))#

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