Mark M. answered • 02/22/21

Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.

The derivative of f^{-1} at f(a) is the reciprocal of the derivative of f(x) at x = a.

So, since f'(a) = 0, the derivative of f^{-1} at f(a) is 1/0, which is undefined.