Answer:
Average rate of change = [tex]\frac{15}{2}[/tex]
Step-by-step explanation:
For a closed interval [tex][a,b][/tex] in a function, the average rate of change is [tex]m=\frac{f(b)-f(a)}{b-a}[/tex].
Thus, given our interval of [tex][1,2][/tex] from the directions, we determine that [tex]f(b)=f(2)=-\frac{10}{(2)^2}=-\frac{10}{4}=-\frac{5}{2}[/tex] and [tex]f(a)=f(1)=-\frac{10}{(1)^2}=-\frac{10}{1}=-10[/tex].
Hence, [tex]m=\frac{f(b)-f(a)}{b-a}=\frac{(-\frac{5}{2})-(-10) }{2-1}=\frac{\frac{15}{2}}{1}=\frac{15}{2}[/tex].
In conclusion, the average rate of change of the function from x=1 to x=2 is [tex]\frac{15}{2}[/tex].
