Since the function f(x) has exactly one global minima and one global maxima, f’(x) is guaranteed to be zero on those x.
Also, since f’(x) is zero for two distinct points, we can apply rolle’s theorem since f’(x0) = f’(x1) = 0 ( x0,x1 are points of global maxima and minima).
So, we could find a point d in the interval [x0,x1] or [x1,x0] such that f’’(d) = 0.
Rolle’s theorem only guarantees a point and not the number of such points. So, it could be more than one too.