Question

Find the average rate of change of the function from x=1 to x=2. f(x)=−18x2

Answer 1

Given function is

$f(x)=-\frac{18}{x^2}$

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

Now,

$\begin{gathered} f(1)=-18 \\ f(2)=-\frac{18}{4} \end{gathered}$

So, the averag erate of change is

$\begin{gathered} \frac{f(2)-f(1)}{2-1}=\frac{-\frac{18}{4}-(-18)}{2-1} \\ =\frac{18-\frac{18}{4}}{1} \\ =\frac{54}{4} \\ =13.5 \end{gathered}$

So, the average rate of change is 13.5.