How do you find the average rate of change of the function #F(x)=x^2-6x+5# over the interval [-2, -2+h]?

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Answer 1 · 2016-09-26T19:30:06

#" The Rate="h-10#.

By Defn., the Average rate of Change of a fun. #F : [a,b] rarr RR#, is

#(F(b)-F(a))/(b-a)#.

Hence, the Reqd. Rate#={F(-2+h)-F(-2)}/(-2+h-(-2))#

#={F(h-2)-F(-2)}/h#

#=[(h-2)^2-6(h-2)+5-{(-2)^2-6(-2)+5}]/h#

#=(h^2-4h+4-6h+12+5-4-12-5)/h#

#=(h^2-10h)/h#

#={h(h-10)}/h#

#:." The Rate="h-10#.