Look at the image of the table of values below. Over which interval of x is the average rate of change the largest?

Between 5 & 8.
[tex]\displaystyle {21-15\over 8-5} = 6/3 = 2[/tex] is the largest rate of change, differentiating from [tex]5\over3[/tex] and [tex]11\over6[/tex]