Given the function h ( x ) = x 2 − 7 x + 7 h(x)=x 2 −7x+7, determine the average rate of change of the function over the interval 2 ≤ x ≤ 9 2≤x≤9.

Sometimes I find it easier to let a calculator evaluate the function for me. The average rate of change is the change in output value divided by the change in input value. That is
.. average rate of change = (f(9) -f(2))/(9 -2)
For this function, this evaluates to
.. average rate of change = (25 -(-3))/(9 -2) = 28/7 = 4

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The graph shows the two points of interest connected by a line of slope 4, verifying our value for the average rate of change.

P(chicago, illinois)