It can be said that the minimum distance of this curve from the origin is the distance of the point from the curve along the normal drawn to the curve passing through the given point,
Now consider a point on this curve,
The equation of the tangent to the curve passing through this point is thus,
Now since the normal to the curve at the given point has to be made to pass through the origin,
Its equation would be of the form ,
Now since it's normal to the given tangent,
Now the intersection of the tangent and normal is at the point t, so that,
Now it's required to solve this above equation.
(Is use of a calculator allowed?)
If yes, then by a little inspection, we can estimate that the root for the above relation lies roughly between -.4265 and -.426.
Since the answer is required upto 2 significant digits only, -.426 can be assumed to be the correct value of t in the above case.
So use x=-.426 in the equation for distance, the answer comes out be approximately 0.78