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Answer 1 · 2016-03-26T13:06:15

Any pair where #f(6)# is #6# greater than #f(3)#.

The average rate of change of the function #f(x)# on the interval from #[a,b]# is equivalent to

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

Since we know this is equal to #2#, and that our interval is #[3,6]#, we can say that

#(f(6)-f(3))/(6-3)=2#

#(f(6)-f(3))/3=2#

#f(6)-f(3)=6#

Thus, any pair of values where #f(6)# is #6# greater than #f(3)# will work. I can't see your answer options, but the pair might be something like:

#{(f(3)=0),(f(6)=6):}#

You could also have any of the following pairs. (Remember, the only thing that must hold true is that #f(6)=6+f(3)#.)

#{(f(3)=-2),(f(6)=4):}#

#{(f(3)=1/2),(f(6)=13/2):}#

#{(f(3)=-200),(f(6)=-194):}#

#{(f(3)=pi),(f(6)=pi+6):}#