Question

the function is graphed below. On which interval of X is the average rate of change of the function the greatest?

Answer 1

Between x = 48 and x = 45.

Explanation:

Average rate of change of a function in the given interval is represented by,

Average rate of change =
`(\triangle y)/(\triangle x)`

From the table attached,

Average rate of change of the function between x = 3 and x = 9

=
`(16-7)/(9-3)`

= 3

Average rate of change in the interval x = 9 and x = 22

=
`(32-16)/(22-9)`

=
`(16)/(13)`

= 1.23

Average rate of change in the interval x = 9 and x = 22,

=
`(45-32)/(45-22)`

=
`(13)/(23)`

= 0.57

Average rate of change in the interval x = 45 and x = 48,

=
`(63-45)/(48-45)`

= 6

Therefore, average rate of change is maximum between x = 45 and 48.

Option given in bottom right will be the answer.