Question

How do you find an equation of the tangent line to the graph of `f(x) = 1/(x-1)` at the point (2,1)?

Answer 1

Since `f(x)=(x-1)^{-1}`, `f'(x)=-(x-1)^{-2}=-1/((x-1)^2)` so that `f'(2)=-1`.

Since `f(2)=1`, the equation of the tangent line is `y=f'(2)(x-2)+f(2)=-(x-2)+1=-x+3`