Let f:R→Rbe a differentiable and increasing function ∀x∈R. If the tangent drawn to the curve at any point x∈(a,b) always lies below the curve, then

Clearly , for f′(x)>0,f′′(x)>0 [in Figure (c)], tangent always lies below the graph. For f′(x)<0,f′′(x)>0 [in Figure (d)], tangent always lies below the graph.