How do you find the average rate of change of #y = x^2 + 7x# over [1,8]?

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Answer 1 · 2016-01-02T17:05:06

#16#

The average rate of change is the slope on that interval.

The slope, or rise over run, measures the change in #y#-values over the change in #x#-values.

The #y#-values are #f(1)# and #f(8)# and the #x#-values are #1# and #8#.

Thus, the average rate of change is equal to

#(f(1)-f(8))/(1-8)#

Find #f(1)# and #f(8)#.

#f(1)=1^2+7(1)=8#

#f(8)=8^2+7(8)=120#

Thus, the average rate of change is equal to

#(8-120)/(1-8)=(-112)/(-7)=16#