Given the function f(x) defined as:
[tex]f(x)=-\frac{14}{x^2}[/tex]
In general, to find the average rate of change of the function from x = a and x = b (a < b), we use the formula:
[tex]Av=\frac{f(b)-f(a)}{b-a}[/tex]
For this problem, a = 1 and b = 2. Then, we calculate f(1) and f(2) first:
[tex]\begin{gathered} f(1)=-\frac{14}{1^2}=-14 \\ f(2)=-\frac{14}{2^2}=-3.5 \end{gathered}[/tex]
Finally, using the formula for the average rate of change:
[tex]Av=\frac{-3.5-(-14)}{2-1}=\frac{-3.5+14}{1}=10.5[/tex]
