Chapter 5.9, Problem 106E

PUTNAM EXAM CHALLENGE

Prove or disprove: there is at least one straight line normal to the graph of $y=\cosh x$ at a point (a, cosh a) and also normal to the graph of $y=\sinh x$ at a point (c, sinh c).

[ At a point on a graph, the normal line is the perpendicular to the tangent at that point. Also, $\cosh x=(e^x+e^{-x})/2$ and $\sinh x=(e^x-e^{-x})/2$.]