Question

What is the equation of the tangent line of `f(x) = 4/(x-1)` at `x=0`?

Answer 1

`y=-4x-4`

Explanation:

Find the derivative of the function and find `f'(0)` at the point `(0,-4)`.

`f(x)=4(x+1)^-1`

`f'(x)=-4(x-1)^-2=-4/(x-1)^2`

`f'(0)=-4/(0-1)^2=-4`

The equation of a line with slope `-4` that passes through `(0,-4)`:

`y=-4x-4`