Question

Find the point(s) on the curve of xy=1 at which the curvature is largest.

Answer 1

x y = 1
y = 1 / x
This function is odd.
The points on the curve at which the curvature is largest:
y = x
x = 1/x
x² = 1
x = +/- √1
x 1 = - 1, x 2 = 1
The points are:
( - 1 , - 1 ) and ( 1, 1 )