Question

Determine the instantaneous rate of change without using derivatives please

Answer 1

we have the function

`f(x)=(x)/(x-2)`

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

For x=0

`f(0)=(0)/(0-2)=0`

The first point is (0,0)

For x=-1

`f(-1)=(-1)/(-1-2)=(1)/(3)`

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

Find out the slope

`\begin{gathered} m=((1)/(3)-0)/(-1-0) \\ \\ m=-(1)/(3) \end{gathered}`

therefore

The instantaneous rate of change is -0.33

Verify the answer with the exact answer (with derivative)