Find the point on the curve farthest from the line $x-y=0$. the curve $x^3-y^3=1$ is asymptote to the line $x-y=0$. Find the point on the curve farthest from the line $x-y=0$.can someone please explain it to me what the question is demanding?
I cant think it geometrically as I am not able to plot it
Also is there any software to plot such graphs.?

Since I don't have a good-enough ( or high -enough ) reputation, I will write my thoughts here:
You have two sets of points in the plane, $S_1=(x,x)$ and EDIT $S_2=(x,(x^3-1)^{1/3})  $
Now use the Euclidean distance and minimize the distance.
