Question

Find the average rate of change of the function from x=1 to x=2.

Answer 1

Answer:

Average rate of change = $\frac{15}{2}$

Step-by-step explanation:

For a closed interval $[a,b]$ in a function, the average rate of change is $m=\frac{f(b)-f(a)}{b-a}$.

Thus, given our interval of $[1,2]$ from the directions, we determine that $f(b)=f(2)=-\frac{10}{(2)^2}=-\frac{10}{4}=-\frac{5}{2}$ and $f(a)=f(1)=-\frac{10}{(1)^2}=-\frac{10}{1}=-10$.

Hence, $m=\frac{f(b)-f(a)}{b-a}=\frac{(-\frac{5}{2})-(-10) }{2-1}=\frac{\frac{15}{2}}{1}=\frac{15}{2}$.

In conclusion, the average rate of change of the function from x=1 to x=2 is $\frac{15}{2}$.