We discuss a concavity like property for functions u satisfying Dα0+ u ∈ C[0, b] with u(0) = 0 and−Dα0+ u(t) ≥ 0 for all t ∈ [0, b]. We develop the property for α ∈ (1, 2], where Dα0+ is the standard Riemann- Liouville fractional derivative. We observe the property is also valid in the case α = 1. Finally, we show that under certain conditions, −Dα0+ u(t) ≥ 0 implies u is concave in the classical sense