Question

Determine the instantaneous rate of change without using derivatives please

Answer 1

we have the function

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

To find out the instantaneous rate of change without using derivatives, we need two points

For x=0

$f(0)=\frac{0}{0-2}=0$

The first point is (0,0)

For x=-1

$f(-1)=\frac{-1}{-1-2}=\frac{1}{3}$

The second point is (-1,1/3)

Find out the slope

$\begin{gathered} m=\frac{\frac{1}{3}-0}{-1-0} \\ \\ m=-\frac{1}{3} \end{gathered}$

therefore

The instantaneous rate of change is -0.33

Verify the answer with the exact answer (with derivative)