Answer: C. 0.19
Step-by-step explanation:
The average rate of change in a function f(x) from x=a to x=b is given by :-
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given function, [tex]f(x)=\sqrt{x-4}[/tex]
The average rate of change in a function f(x) from x=8 to x=14 is given by :-
[tex]\dfrac{f(14)-f(8)}{14-8}=\dfrac{\sqrt{14-4}-\sqrt{8-4}}{6}\\\\=\dfrac{\sqrt{10}-\sqrt{4}}{6}\\\\\approx\dfrac{3.16-2}{6}\\\\=\dfrac{1.16}{6}=0.193333333333\approx0.19[/tex]
Thus , the average rate of change of f(x) from 8 to 14 is 0.19. (approx)
Hence, the correct option is C. 0.19
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