Question #c15cb

Question

1311 views around the world

You can reuse this answer
Creative Commons License

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 $f(6)=6+f(3)$ .)

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

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

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

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