Given the functions f(x) and g(x):
The function f(x) given a table:
x -2, -1, 0, 1, 2, 3
f(x) -12, -10, -6, 0, 8, 18
And the function g(x) = 3x² - 14
We will find the average rate of change of f(x) and g(x) on the interval [0, 2]
The average rate of change of f(xt will be as follows:
[tex]\frac{f(2)-f(0)}{2-0}=\frac{8-(-6)}{2-0}=\frac{14}{2}=7[/tex]The average rate of change of g(x) will be as follows:
[tex]\begin{gathered} g(2)=3(2)^2-14=-2 \\ g(0)=3(0)^2-14=-14 \\ \\ \frac{g(2)-g(0)}{2-0}=\frac{-2-(-14)}{2-0}=\frac{12}{2}=6 \end{gathered}[/tex]As shown from the results:
Both functions are increasing.
The average rate of f(x) > the average rate of g(x)
The true statement will be:
Function f increases at a faster rate than function g on the interval [0, 2]
