How do you find the average rate of change of #f(x)= -2/(3x+5)# over [-1,3]?

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Answer 1 · 2017-04-30T06:55:48

The answer is #=3/14#

The average rate of change of a function #f(x)# over the interval #[a, b]# is

#=(f(b)-f(a))/(b-a)#

Here, we have

#f(x)=-2/(3x+5)#

and the interval is #[-1,3]#

so,

#f(3)=-2/(3*3+5)=-2/14=-1/7#

#f(-1)=-2/(3*-1+5)=-2/2=-1#

So,

The average rate of change is

#=(f(3)-f(-1))/(3-(-1))=(-1/7+1)/(3+1)=6/7*1/4=3/14#