TITLE: When $dy/dx =0$ for all $x$ in the domain, is $dx/dy$ also zero?
QUESTION [5 upvotes]: If $dy/dx = 0$ for all $x$ in the domain, is $dx/dy$ also zero? This seems problematic because $dy/dx$ can be thought as $0/1 = 0$ but when you reverse the upper and lower part of the fraction, the fraction is an invalid number.

REPLY [9 votes]: If $\frac{dy}{dx}=0$ in an open interval, then $y$ is constant in that interval, so one does not have an inverse function $x$ of $y$.