How do you find the average rate of change of #y=-1/(x-2)# over [-3,-2]?

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How do you find the average rate of change of #y=-1/(x-2)# over [-3,-2]?

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Answer 1 · 2016-12-21T11:57:41

The average rate of change of #y=−1/(x−2)# over #[-3,-2]# equals #1/20#

Explanation:

The rate of change of #y(x)# over the interval #[x_1,x_2]# is defined as the ratio between the variation of #y(x)# and the variation of #x# over the interval, so that:

#R= (Deltay)/(Deltax) = (y(x_2)-y(x_1))/(x_2-x_1)#

In our case:

#R = ((-1/(-2-2))-(-1/(-3-2)))/((-2)-(-3))= (1/4-1/5)=1/20#

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How do you find the average rate of change of #y=-1/(x-2)# over [-3,-2]?

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