How do you find the average rate of change of #y=x^3+1# from #x=1# to #x=3#?

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Answer 1 · 2014-09-19T08:28:59

#(f(x+h)-f(x))/h=(f(b)-f(a))/(b-a)#, where #a# is the lower bound and #b# is the upper bound.

Average rate of change

#slope=(f(b)-f(a))/(b-a)=(f(3)-f(1))/(3-1)=((3)^3+1-((1)^3+1))/(3-1)=((27+1)-(1+1))/(3-1)=(28-2)/(3-1)=26/2=13#

Point: #(3,28)#
Point: #(1,2)#

#y=mx+b#

#2=13(1)+b#

#2=13+b#

#-11=b#

#y=13x-11#, the secant line through the points #(3,28)# and #(1,2)#.