Answer:
C
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 the closed interval is [ 3, 7 ]
f(b) = f(7) = [tex]\frac{47}{6}[/tex]
f(a) = f(3) = [tex]\frac{17}{2}[/tex]
f(7) - f(3) = [tex]\frac{47}{6}[/tex] - [tex]\frac{17}{2}[/tex] = - [tex]\frac{2}{3}[/tex]
Thus
[tex]\frac{-\frac{2}{3} }{7-3}[/tex]
= [tex]\frac{-\frac{2}{3} }{4}[/tex]
= - [tex]\frac{2}{3}[/tex] × [tex]\frac{1}{4}[/tex] = - [tex]\frac{1}{6}[/tex]
Average rate of change = - [tex]\frac{1}{6}[/tex] → C
