Question

Is `f(x)=-x/(x-5)` increasing or decreasing at `x=-1`?

Answer 1

`f(x)=-(x)/(x-5)` is always increasing.

Explanation:

`f(x)=-(x)/(x-5)=-(x-5+5)/(x-5)=-1-5*1/(x-5)`

hence `f'(x)=-5*((-1)/(x-5)^2)=5/(x-5)^2`

As `f'(x)>=0` for all `x`

`f(x)=-(x)/(x-5)` is always increasing.

graph{-(x)/(x-5 [-10, 10, -5, 5]}