Answer:
D
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 ] = [ 3, 5 ]
f(b) = f(5) = [tex]\frac{5^{2} }{4}[/tex] - 5 = [tex]\frac{25}{4}[/tex] - [tex]\frac{20}{4}[/tex] = [tex]\frac{5}{4}[/tex]
f(a) = f(3) = [tex]\frac{3^{2} }{4}[/tex] - 5 = [tex]\frac{9}{4}[/tex] - [tex]\frac{20}{4}[/tex] = - [tex]\frac{11}{4}[/tex]
Hence
average rate of change = [tex]\frac{5/4+11/4}{5-3}[/tex] = [tex]\frac{4}{2}[/tex] = 2
