For vector-valued functions with V a finite-dimensional normed space, there is no analogue of the equality above, indeed it fails. But since inf f ′ ′ ≤ ≤ f ′ ′ ( c ) ≤ ≤ sup f ′ ′ , the inequality above is a useful substitute. Moreover, using the pairing of the dual of V with its dual norm, yields the following inequality: