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

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

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