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

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Answer 1 · 2016-09-11T13:39:17

#2/3#.

Let #y=f(x)=-1/(x+2), x in [-1,-1/2]#.

By Defn., the Average Rate of Change of #y" over "[-1,-1/2]#

#=(f(-1/2)-f(-1))/(-1/2-(-1))=(f(-1/2)-f(-1))/(1/2)=2{f(-1/2)-f(-1)}#.

#=2{(-1/(-1/2+2))-(-1/(-1+2))}#

#=2{-1/(3/2)+(1/1)}#

#=2(-2/3+1)#

#=2(1/3)#

#=2/3#.