How do you find the average rate of change of f(x)= -2/(3x+5)f(x)=−23x+5 over [-1,3]?

1 Answer
Narad T.
Apr 30, 2017

The answer is =3/14=314

Explanation:

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

=(f(b)-f(a))/(b-a)=f(b)−f(a)b−a

Here, we have

f(x)=-2/(3x+5)f(x)=−23x+5

and the interval is [-1,3][−1,3]

so,

f(3)=-2/(3*3+5)=-2/14=-1/7f(3)=−23⋅3+5=−214=−17

f(-1)=-2/(3*-1+5)=-2/2=-1f(−1)=−23⋅−1+5=−22=−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=f(3)−f(−1)3−(−1)=−17+13+1=67⋅14=314

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