Question

What is the instantaneous rate of change of `f(x)=1/(x-7 )` at `x=0`?

Answer 1

`-1/49`

Explanation:

The `color(blue)"instantaneous rate of change"` derives from the value of f'(0).

`f(x)=1/(x-7)=(x-7)^-1`

`rArrf'(x)=-1(x-7)^-2.d/dx(x-7)=-(x-7)^-2 .1=-1/(x-7)^2`

and `f'(0)=-1/(0-7)^2=-1/49`