Determine a rational curve and sketch its derivative exactly

The curve $C$ is $y=f(x)=\dfrac{ax^2+b}{x+c}$, where $a,b,c$ are constants, and $y=-x+2$ is an asymptote.

(i) Show that $a=-1$, $c=2$.2 marks

(ii) Given $b=1$, sketch $C$, showing all asymptotes, stationary points and axial intercepts, if any.4 marks

(iii) Sketch $y=f^{\prime}(x)$, showing all asymptotes, axial intercepts and stationary points, if any.3 marks