Answer:
- [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ - 1, 3 ] , then
f(3) = [tex]\frac{1}{3-5}[/tex] = - [tex]\frac{1}{2}[/tex]
f(- 1) = [tex]\frac{1}{-1-5}[/tex] = - [tex]\frac{1}{6}[/tex]
average rate of change
= [tex]\frac{-\frac{1}{2}-(-\frac{1}{6}) }{3-(-1)}[/tex]
= [tex]\frac{-\frac{1}{2}+\frac{1}{6} }{3+1}[/tex]
= [tex]\frac{-\frac{1}{3} }{4}[/tex]
= - [tex]\frac{1}{12}[/tex]
