Answer:
Function g(x) has the greater average rate of change over the given interval.
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\sf \dfrac{f(b)-f(a)}{b-a}[/tex]
Given:
Therefore, the average rate of change for the function f(x) over the given interval 4 ≤ x ≤ 8 is:
[tex]\sf \implies\dfrac{f(8)-f(4)}{8-4}=\dfrac{14-0}{8-4}=3.5[/tex]
Work out values of function g(x) for x = 4 and x = 8:
[tex]\implies \sf g(4)=2(4)^2+(4)-1=35[/tex]
[tex]\implies \sf g(8)=2(8)^2+(8)-1=135[/tex]
Therefore, the average rate of change for the function g(x) over the given interval 4 ≤ x ≤ 8 is:
[tex]\implies \sf \dfrac{g(8)-g(4)}{8-4}=\dfrac{135-35}{8-4}=\dfrac{100}{4}=25[/tex]
Therefore, function g(x) has the greater average rate of change over the interval 4 ≤ x ≤ 8, as 25 > 3.5.