$f\left(x\right)=k\left(x-1\right)^3-1, \ k<0$ $f=f^{-1} \ \text{has pairs of intersections} \ \left(x,y\right), \ \left(y,x\right), \ x\ne y$ $\text{Lines in form of} \ y=-x+c \ \text{can be formed with a pair of such points}$ $\text{Find} \ k \ \text{that gives maximum perpendicular distance of such lines}$
In other words, I want to find when this is length max
